Deck 6: Probability in Statistics

Question 1

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Rolling a 4 with a fair die

A)Event
B)Outcome

Answer 1

Outcome

Question 2

Interpret the level of statistical significance for the event described.

-A study of students taking Statistics 101 was done. 500 students who studied for more than 10 hours averaged a B. 250 students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 Level. What does this mean?

A)There is not enough information to make any conclusion.
B)The probability that the difference was due to chance alone is greater than 0.01.
C)The improvement was due to the fact that more people studied.
D)There is less than a 0.01 chance that the grades were better by chance alone.

Answer 2

There is less than a 0.01 chance that the grades were better by chance alone.

Question 3

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Tossing five tails with five fair coins

A)Event
B)Outcome

Answer 3

Outcome

Question 4

Interpret the level of statistical significance for the event described.

-A national survey was done. It showed that a sample of 605 men aged 25-34 watched an average of 9 hours of television a week. A sample of 503 men aged 45-54 watched an average of 19 hours of television a
Week. This difference is significant at the 0.05 level. Interpret the result.

A)There is not enough information to make any conclusion.
B)The probability that the difference was due to chance alone is greater than 0.05.
C)The probability is less than 0.05 that the older group watches more television by chance alone.
D)The older group watches more television because they have more televisions.

Question 5

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Tossing one head and one tail with two fair coins

A)Event
B)Outcome

Question 6

For the given event, state whether the difference between what occurred and what you would have expected by chance is statistically significant or not statistically significant.

-You are told that a mystery person's name begins with a consonant, and you correctly guess the first letter of
That mystery person's name.

A)statistically significant
B)not statistically significant

Question 7

For the given event, state whether the difference between what occurred and what you would have expected by chance is statistically significant or not statistically significant.

-Assume that a study of 500 randomly selected school bus routes showed that 486 of the buses arrived on time.
One of the buses, however, was late.

A)statistically significant
B)not statistically significant

Question 8

For the given event, state whether the difference between what occurred and what you would have expected by chance is statistically significant or not statistically significant.

-Assume that a study of 300 randomly selected school bus routes showed that 277 of the buses arrived on time. One of the buses, however, was late.

A)statistically significant
B)not statistically significant

Question 9

Interpret the level of statistical significance for the event described.

-A study of two types of weed killers was done. One weed killer killed 45% more weeds than the other. This difference was significant at the 0.05 level. What does this mean?

A)The probability that one weed killer performed better by chance alone is less than a 0.05.
B)The probability that the difference was due to chance alone is greater than 0.05.
C)The improvement was due to the fact that there were more weeds in one study.
D)There is not enough information to make any conclusion.

Question 10

For the given event, state whether the difference between what occurred and what you would have expected by chance is statistically significant or not statistically significant.

-A person tells you the day of the week he was born, and you correctly guess the month and day of his birth.

A)statistically significant
B)not statistically significant

Question 11

For the given event, state whether the difference between what occurred and what you would have expected by chance is statistically significant or not statistically significant.

-A multiple choice question has 19 possible answers, only one of which is correct. A student makes a random guess on the question and is correct.

A)statistically significant
B)not statistically significant

Question 12

For the given event, state whether the difference between what occurred and what you would have expected by chance is statistically significant or not statistically significant.

-After 36 rolls of two six-sided dice, the numbers on the dice add to 6 two times.

A)statistically significant
B)not statistically significant

Question 13

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Drawing three jacks from a regular deck of cards

A)Event
B)Outcome

Question 14

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Drawing a queen and then the king of diamonds from a regular deck of cards

A)Event
B)Outcome

Question 15

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Rolling a sum of 12 with two fair dice

A)Event
B)Outcome

Question 16

Interpret the level of statistical significance for the event described.

-A study of 600 college students taking Statistics 101 revealed that 59 students received the grade of A.
Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case?

A)The probability that the difference occurred due to chance is more than 0.05.
B)The probability that the difference occurred due to chance is less than 0.05.
C)There is not enough information to make any conclusion.
D)The probability of getting an A is 10% and only 9% got an A in this study. The difference is less than 5% so it is not significant.

Question 17

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Drawing a black six and then a black seven from a regular deck of cards

A)Event
B)Outcome

Question 18

For the given event, state whether the difference between what occurred and what you would have expected by chance is statistically significant or not statistically significant.

-In 36 rolls of two six-sided dice, the numbers on the dice add to 12 twelve times.

A)statistically significant
B)not statistically significant

Question 19

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Rolling at least one 2 with two fair dice

A)Event
B)Outcome

Question 20

For the observation described, state whether there is one way for the given observation to occur (outcome)or more thanone way for the given observation to occur (in which case it is an event).

-Tossing two tails with three fair coins

A)Event
B)Outcome

Question 21

Find the indicated probability.

-If two balanced dice are rolled, the possible outcomes can be represented as follows. $( 1,1 ) ( 2,1 ) ( 3,1 ) ( 4,1 ) ( 5,1 ) ( 6,1 )$
$( 1,2 ) ( 2,2 ) ( 3,2 ) ( 4,2 ) ( 5,2 ) ( 6,2 )$
$( 1,3 ) ( 2,3 ) ( 3,3 ) ( 4,3 ) ( 5,3 ) ( 6,3 )$
$( 1,4 ) ( 2,4 ) ( 3,4 ) ( 4,4 ) ( 5,4 ) ( 6,4 )$
$( 1,5 ) ( 2,5 ) ( 3,5 ) ( 4,5 ) ( 5,5 ) ( 6,5 )$
$( 1,1 ) ( 2,1 ) ( 3,1 ) ( 4,1 ) ( 5,1 ) ( 6,1 )$
$( 1,2 ) ( 2,2 ) ( 3,2 ) ( 4,2 ) ( 5,2 ) ( 6,2 )$
$( 1,3 ) ( 2,3 ) ( 3,3 ) ( 4,3 ) ( 5,3 ) ( 6,3 )$
$( 1,4 ) ( 2,4 ) ( 3,4 ) ( 4,4 ) ( 5,4 ) ( 6,4 )$
$( 1,5 ) ( 2,5 ) ( 3,5 ) ( 4,5 ) ( 5,5 ) ( 6,5 )$
$( 1,6 ) ( 2,6 ) ( 3,6 ) ( 4,6 ) ( 5,6 ) ( 6,6 )$

Determine the probability that the sum of the dice is $9 .$

A) $\frac { 5 } { 36 }$

B) $\frac { 1 } { 9 }$

C) $\frac { 1 } { 6 }$

D) $\frac { 1 } { 12 }$

Question 22

Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. What is the probability that the family has at least one boy?

A)0.857
B)0.75
C)0.125
D)0.875

Question 23

Find the indicated probability.

-On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

A) 0
B) $\frac { 1 } { 6 }$
C) 1
D) 6

Question 24

In a poll, respondents were asked whether they had ever been in a car accident. 204 respondents indicated thatthey had been in a car accident and 365 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident?
Round to the nearest thousandth, if necessary.

A)0.641
B)0.559
C)0.005
D)0.359

Question 25

Find the indicated probability.

-A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected atrandom from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of thepossible outcomes (for example RB represents the outcome red chip followed by blue chip)and use your list todetermine the probability that one blue chip and one green chip are selected.

A) $\frac { 1 } { 4 }$

B) $\frac { 1 } { 2 }$

C) $\frac { 1 } { 16 }$

D) $\frac { 1 } { 8 }$

Question 26

Find the indicated probability.

-A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

A) $\frac { 1 } { 11 }$

B) $\frac { 1 } { 5 }$

C) $\frac { 3 } { 14 }$

D) $\frac { 1 } { 3 }$

Question 27

A multiple choice Statistics exam has 10 possible answers for each question, only one of which is correct. If you guess randomly on every question, what score might you expect to get? Express your answer as a percentage.

A)90%
B)50%
C)15%
D)10%

Question 28

Find the indicated probability.

-A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

A) 10
B) $\frac { 11 } { 12 }$

C) $\frac { 1 } { 12 }$

D) $\frac { 5 } { 6 }$

Question 29

Find the indicated probability.

-Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will Be 3?

A) $\frac { 1 } { 18 }$

B) $\frac { 17 } { 18 }$

C) $\frac { 1 } { 2 }$

D) 2

Question 30

Find the indicated probability.

-If two balanced dice are rolled, the possible outcomes can be represented as follows. $( 1,1 ) ( 2,1 ) ( 3,1 ) ( 4,1 ) ( 5,1 ) ( 6,1 )$
$( 1,2 ) ( 2,2 ) ( 3,2 ) ( 4,2 ) ( 5,2 ) ( 6,2 )$
$( 1,3 ) ( 2,3 ) ( 3,3 ) ( 4,3 ) ( 5,3 ) ( 6,3 )$
$( 1,4 ) ( 2,4 ) ( 3,4 ) ( 4,4 ) ( 5,4 ) ( 6,4 )$
$( 1,5 ) ( 2,5 ) ( 3,5 ) ( 4,5 ) ( 5,5 ) ( 6,5 )$
$( 1,6 ) ( 2,6 ) ( 3,6 ) ( 4,6 ) ( 5,6 ) ( 6,6 )$
Determine the probability that the sum of the dice is 4 or 10 .

A) $\frac { 2 } { 9 }$

B) $\frac { 5 } { 36 }$

C) $\frac { 7 } { 36 }$

D) $\frac { 1 } { 6 }$

Question 31

Find the indicated probability.

-A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.)

A) $\frac { 1 } { 2 }$

B) $\frac { 2 } { 5 }$

C) $\frac { 3 } { 5 }$

D) $\frac { 7 } { 10 }$

Question 32

Find the indicated probability.

-A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example RB represents the outcome red chip followed by blue chip)and use your list to determine the probability that the two chips selected are different colors.
(Hint: There are 16 possible outcomes.)

A) $\frac { 3 } { 8 }$

B) $\frac { 3 } { 4 }$

C) $\frac { 1 } { 2 }$

D) $\frac { 3 } { 16 }$

Question 33

Find the indicated probability.

-If a person is randomly selected, find the probability that his or her birthday is in December. Ignore leap years.

A) $\frac { 1 } { 31 }$

B) $\frac { 1 } { 365 }$

C) $\frac { 31 } { 365 }$

D) $\frac { 1 } { 12 }$

Question 34

Find the indicated probability.

-Sammy and Sally each carry a bag containing a banana, a chocolate bar, and a licorice stick. Simultaneously, they take out a single food item and consume it. The possible pairs of food items that Sally and Sammy consumed are as follows.

chocolate bar - chocolate bar
licorice stick - chocolate bar
banana - banana
chocolate bar - licorice stick
licorice stick - licorice stick
chocolate bar - banana
banana - licorice stick
licorice stick - banana
banana - chocolate bar

Find the probability that at least one banana was eaten.

A) $\frac { 4 } { 5 }$

B) $\frac { 5 } { 9 }$

C) $\frac { 7 } { 9 }$

D) $\frac { 1 } { 3 }$

Question 35

Determine the probability of the given opposite event.

-If $\mathrm { P } ( \mathrm { A } ) = \frac { 6 } { 11 }$ , find $\mathrm { P } ( \overline { \mathrm { A } } )$ .

A) $\frac { 6 } { 17 }$

B) $\frac { 11 } { 6 }$

C) $\frac { 5 } { 11 }$

D) 0

Question 36

Find the indicated probability.

-If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head?

A) $\frac { 7 } { 8 }$

B) $\frac { 1 } { 4 }$

C) $\frac { 1 } { 2 }$

D) $\frac { 3 } { 4 }$

Question 37

Find the indicated probability.

-If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What isthe probability of getting at least two heads?

A) $\frac { 1 } { 8 }$

B) $\frac { 5 } { 8 }$

C) $\frac { 1 } { 2 }$

D) $\frac { 3 } { 8 }$

Question 38

Find the indicated probability.

-A class consists of 41 women and 37 men. If a student is randomly selected, what is the probability that the
Student is a woman?

A) $\frac { 41 } { 78 }$

B) $\frac { 41 } { 37 }$

C) $\frac { 1 } { 78 }$

D) $\frac { 37 } { 78 }$

Question 39

Find the indicated probability.

-A committee of three people is to be formed. The three people will be selected from a list of five possible committeemembers. A simple random sample of three people is taken, without replacement, from the group of five people. If thefive people are represented by the letters A, B, C, D, E, the possible outcomes are as follows.
$\begin{array}{l}\mathrm{ABC} \\\mathrm{ABD} \\\mathrm{ABE} \\\mathrm{ACD} \\\mathrm{ACE} \\\mathrm{ADE} \\\mathrm{BCD} \\\mathrm{BCE} \\\mathrm{BDE}\end{array}$

Determine the probability that B and C are both included in the sample.

A) $\frac { 3 } { 10 }$

B) $\frac { 1 } { 10 }$

C) $\frac { 9 } { 10 }$

D) $\frac { 2 } { 10 }$

Question 40

Find the indicated probability.

-If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that the first two tosses come up the same?

A) $\frac { 3 } { 8 }$

B) $\frac { 1 } { 8 }$

C) $\frac { 1 } { 2 }$

D) $\frac { 1 } { 4 }$

Question 41

The distribution of B.A. degrees conferred by a local college is listed below, by major. What is the probability that a randomly selected degree is not in Physics?

A)0.092
B)0.908
C)0.966
D)0.907

Question 42

Determine the probability of the given opposite event.

Question 43

The probability that Luis will pass his statistics test is 0.86. Find the probability that he will fail his statistics test.

A)6.14
B)1.16
C)0.43
D)0.14

Question 44

What is the probability of getting anything except 5 tails when you toss five fair coins at once?

A) $\frac { 1 } { 2 }$

B) $\frac { 1 } { 32 }$

C) $\frac { 30 } { 32 }$

D) $\frac { 31 } { 32 }$

Question 45

If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

A) $\frac { 334 } { 365 }$

B) $\frac { 31 } { 334 }$

C) $\frac { 11 } { 12 }$

D) $\frac { 31 } { 365 }$

Question 46

What is the probability of getting two tails and one head when you toss three fair coins at once?

A) $\frac { 1 } { 4 }$

B) $\frac { 1 } { 8 }$

C) $\frac { 3 } { 8 }$

D) $\frac { 1 } { 2 }$

Question 47

Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.185. Find the probability that in a given year it will not snow on January 1st in that town.

A)1.185
B)0.815
C)0.227
D)5.405

Question 48

What is the probability of getting anything except 3 tails when you toss three fair coins at once?

A) $\frac { 1 } { 2 }$

B) $\frac { 3 } { 8 }$

C) $\frac { 7 } { 8 }$

D) $\frac { 1 } { 8 }$

Question 49

Assume five fair coins are tossed at once. Construct a table showing the probability distribution for the events 5 heads, 4
Heads, 3 heads, 2 heads, 1 head, and 0 heads.. $\quad$ $\quad$
$\text { Tossing } 5 \text { Coins }$
$\begin{array}{lll}\hline\text { Result } &\text { Probability }\\\hline \\\\\\\\\\\\\hline\text { Total }&&\\\end{array}$

A)
$\quad$ $\quad$$\text { Tossing } 5 \text { Coins }$
$\begin{array}{llc}\hline\text { Result } &&\text { Probability }\\\hline5 \text { heads } & 0 \text { tails } & 1 / 6 \\4 \text { heads } & 1 \text { tail } & 1 / 6 \\3 \text { heads } & 2 \text { tails } & 1 / 6 \\2 \text { heads } & 3 \text { tails } & 1 / 6 \\1 \text { head } & 4 \text { tails } & 1 / 6 \\0 \text { heads } & 5 \text { tails } & 1 / 6\\\hline\\\text { Total }&&1\\\hline \end{array}$


B)
$\quad$ $\quad$$\text { Tossing } 5 \text { Coins }$
$\begin{array}{clc}\hline\text { Result } &&\text { Probability }\\ \hline5 \text { heads } & 0 \text { tails } & 1 \\4 \text { heads } & 1 \text { tail } & 5 \\3 \text { heads } & 2 \text { tails } & 10 \\2 \text { heads } & 3 \text { tails } & 10 \\1 \text { head } & 4 \text { tails } & 5 \\0 \text { heads } & 5 \text { tails } & 1\\\hline\text {Total}&&32 \end{array}$


C)
$\quad$ $\quad$$\text { Tossing } 5 \text { Coins }$
$\begin{array}{llc}\hline\text { Result } &&\text { Probability }\\\hline5 \text { heads } & 0 \text { tails } & 1 / 32 \\4 \text { heads } & 1 \text { tail } & 5 / 32 \\3 \text { heads } & 2 \text { tails } & 10 / 32 \\2 \text { heads } & 3 \text { tails } & 10 / 32 \\1 \text { head } & 4 \text { tails } & 5 / 32 \\0 \text { heads } & 5 \text { tails } & 1 / 32\\\hline\text { Total }&&1\end{array}$




D)
$\quad$ $\quad$$\text { Tossing } 5 \text { Coins }$
$\begin{array}{llc}\hline\text { Result } &&\text { Probability }\\\hline5 \text { heads } & 0 \text { tails } & 1 \\4 \text { heads } & 1 \text { tail } & 1 \\3 \text { heads } & 2 \text { tails } & 1 \\2 \text { heads } & 3 \text { tails } & 1 \\1 \text { head } & 4 \text { tails } & 1 \\0 \text { heads } & 5 \text { tails } & 1\\\hline\text { Total }&&6\end{array}$

Question 50

The frequency table describes the distribution of birds viewed by a bird watching group. Estimate the probability that the group will see a hawk on the next bird watching trip.

A)0.037
B)0.038
C)0.034
D)0.222

Question 51

The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $82,000.
$\begin{array} { l l l r r l r r r r } 92,000 & 102,000 & 76,000 & 107,000 & 79,000 & 92,000 & 82,000 & 70,000 & 117,000 & 142,000 \\ 112,000 & 79,000 & 102,000 & 97,000 & 82,000 & 122,000 & 67,000 & 97,000 & 73,000 & 87,000 \end{array}$

A) $0.8$
B) $0.4$
C) $0.7$
D) $0.6$

Question 52

Use the relative frequency method to estimate the probability. Round your answer to three decimal places.

-A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 1 = FOR, 2 = AGAINST. If the referendum were held today, estimate the probability that it would pass. $1,2,2,1,1,2,1,2,2,1,1,1,2,1,2,1,1,1,2,1$

A) $0.4$
B) $0.65$
C) $0.5$
D) $0.6$

Question 53

Halfway through the season, a basketball player has hit 61% of her free throws. What is the probability that her
Next free throw will be successful?

A)0.61
B)0.39
C)0.061
D)0.5

Question 54

A family with three children is randomly selected. Assume that births of boys and girls are equally likely. Construct a
Table showing the probability distribution for the events 3 girls, 2 girls, 1 girl, and 0 girls.


$\quad$ $\quad$$3 \text { Child Family }$
$\begin{array}{cc}\hline \text { Result }&\text { Probability }\\\hline \\\\ \\\\\hline\text { Total }\end{array}$

A)
$\quad$ $\quad$$3 \text { Child Family }$
$\begin{array}{cc}\hline \text { Result }&\text { Probability }\\\hline 3 \text { girls } & 0 \text { boys } \\2 \text { girls } & 1 \text { boy } \\1 \text { girl } & 2 \text { boys } \\0 \text { girls } & 3 \text { boys }\\\hline\text { Total }&8\end{array}$


B)
$\quad$ $\quad$$3 \text { Child Family }$
$\begin{array}{cc}\hline \text { Result }&&\text { Probability }\\\hline3 \text { girls } & 0 \text { boys } & 1 \\2 \text { girls } & 1 \text { boy } & 1 \\1 \text { girl } & 2 \text { boys } & 1 \\0 \text { girls } & 3 \text { boys } & 1 \\\hline\text { Total }&&4\end{array}$


C)
$\quad$ $\quad$$3 \text { Child Family }$
$\begin{array}{cc}\hline \text { Result }&&\text { Probability }\\\hline3 \text { girls } & 0 \text { boys } & 1 / 8 \\2 \text { girls } & 1 \text { boy } & 3 / 8 \\1 \text { girl } & 2 \text { boys } & 3 / 8 \\0 \text { girls } & 3 \text { boys } & 1 / 8\\\hline\text { Total }&&1\end{array}$



D)
$\quad$ $\quad$$3 \text { Child Family }$
$\begin{array}{cc}\hline \text { Result }&&\text { Probability }\\\hline3 \text { girls } & 0 \text { boys } & 1 / 4 \\2 \text { girls } & 1 \text { boy } & 1 / 4 \\1 \text { girl } & 2 \text { boys } & 1 / 4 \\0 \text { girls } & 3 \text { boys } & 1 / 4\\\hline\text { Total }&&1\end{array}$

Question 55

Give the appropriate response.

-Construct a table showing all possible outcomes and probabilities of tossing 3 fair coins at once.

A)
$\quad$ $\quad$ $\quad$ $\quad$$\quad$ $\quad$ $\quad$ $\quad$$\underline{\text { Tossing } 3 \text { Coins }}$
$\begin{array}{ccccc}\underline{\text { Coin } 1} &\underline{ \text { Coin } 2 }& \underline{\text { Coin } 3 }&\underline{ \text { Outcome } }&\underline{ \text { Probability }} \\\text { H } & \text { H } & \text { H } & \text { HHH } & 1 / 4 \\\mathrm{H} & \mathrm{H} & \mathrm{T} & \text { HHT } & 1 / 4 \\\mathrm{~T} & \mathrm{~T} & \mathrm{H} & \text { TTH } & 1 / 4 \\\mathrm{~T} & \mathrm{~T} & \mathrm{~T} & \text { TTT } & 1 / 4\end{array}$


B)
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\underline{\text { Tossing } 3 \text { Coins }}$
$\begin{array}{ccccc} \underline{\text { Coin } 1} & \underline{\text { Coin } 2} & \underline{\text { Coin } 3}& \underline{\text { Outcome}}& \underline{ \text { Probability }}\\ \mathrm{H} & \mathrm{H} & \mathrm{H} & \text { HHH } & 1 / 8 \\\mathrm{H} & \mathrm{H} & \mathrm{T} & \text { HHT } & 1 / 8 \\\mathrm{H} & \mathrm{T} & \mathrm{H} & \text { HTH } & 1 / 8 \\\mathrm{H} & \mathrm{T} & \mathrm{T} & \text { HTT } & 1 / 8 \\\mathrm{~T} & \mathrm{H} & \mathrm{H} & \text { THH } & 1 / 8 \\\mathrm{~T} & \mathrm{H} & \mathrm{T} & \text { THT } & 1 / 8 \\\text { T } & \text { T } & \text { H } & \text { TTH } & 1 / 8 \\\text { T } & \text { T } & \text { T } & \text { TTT } & 1 / 8\end{array}$


C)
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\underline{\text { Tossing } 3 \text { Coins }}$
$\begin{array}{ccccc} \underline{\text { Coin } 1} & \underline{\text { Coin } 2} & \underline{\text { Coin } 3}& \underline{\text { Outcome}}& \underline{ \text { Probability }}\\ \text { H } & \text { H } & \text { H } & \text { HHH } & 1 \\\text { H } & \text { H } & \text { T } & \text { HHT } & 1 \\\text { H } & \text { T } & \text { H } & \text { HTH } & 1 \\\text { H } & \text { T } & \text { T } & \text { HTT } & 1 \\\text { T } & \text { H } & \text { H } & \text { THH } & 1 \\\text { T } & \text { H } & \text { T } & \text { THT } & 1 \\\text { T } & \text { T } & \text { H } & \text { TTH } & 1 \\\text { T } & \text { T } & \text { T } & \text { TTT } & 1\end{array}$


D)
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\underline{\text { Tossing } 3 \text { Coins }}$
$\begin{array}{ccccc} \underline{\text { Coin } 1} & \underline{\text { Coin } 2} & \underline{\text { Coin } 3}& \underline{\text { Outcome}}& \underline{ \text { Probability }}\\ \mathrm{H} & \mathrm{H} & \mathrm{H} & \text { HHH } & 1 / 8 \\\mathrm{H} & \mathrm{H} & \mathrm{T} & \text { HHT } & 3 / 8 \\\mathrm{H} & \mathrm{T} & \mathrm{H} & \text { HTH } & 3 / 8 \\\mathrm{H} & \mathrm{T} & \mathrm{T} & \text { HTT } & 3 / 8 \\\mathrm{~T} & \mathrm{H} & \mathrm{H} & \text { THH } & 3 / 8 \\\text { T } & \text { H } & \text { T } & \text { THT } & 3 / 8 \\\text { T } & \text { T } & \text { H } & \text { TTH } & 3 / 8 \\\text { T } & \text { T } & \text { T } & \text { TTT } & 1 / 8\end{array}$

Question 56

Of 1841 people who came into a blood bank to give blood, 218 people had high blood pressure. Estimate the
Probability that the next person who comes in to give blood will have high blood pressure.

A)0.169
B)0.037
C)0.086
D)0.118

Question 57

In a certain class of students, there are 11 boys from Wilmette, 6 girls from Winnetka, 6 girls from Wilmette, 5 boys from Glencoe, 5 boys from Winnetka and 6 girls from Glencoe. If the teacher calls upon a student to
answer a question, what is the probability that the student will be a boy?

A)0.282
B)0.697
C)0.41
D)0.538

Question 58

100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the
Person does not work full time.

1. Public transportation: 6 full time, 8 part time
2. Bicycle: 3 full time, 5 part time
3. Drive alone: 29 full time, 33 part time
4. Carpool: 9 full time, 7 part time

A)0.48
B)0.47
C)0.33
D)0.53

Question 59

In a certain class of students, there are 11 boys from Wilmette, 4 girls from Kenilworth, 10 girls from Wilmette, 4 boys from Glencoe, 5 boys from Kenilworth and 8 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?

A)0.25
B)0.095
C)0.214
D)0.3

Question 60

100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the person does not commute by public transportation.
1. Public transportation: 6 full time, 8 part time
2. Bicycle: 5 full time, 4 part time
3. Drive alone: 26 full time, 33 part time
4. Carpool: 8 full time, 10 part time

A)1.00
B)0.86
C)0.14
D)0.39

Question 61

Find the expected value.
The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one:
$5200 (1 chance in 8900); $2500 (1 chance in 6400); $900 (1 chance in 3900); $100 (1 chance in 2100).
Find the expected value of the amount won for one entry if the cost of entering is 57 cents.

A)$100.00
B)$0.62
C)$1.21
D)$0.68

Question 62

Use the data to find the required rate. Round your answer to thousandths unless indicated otherwise.

-An insurance company reported that last year there were claims for medical expenses for 2669 on-the-job injuries. The company covers 327,171 employees. Find the rate of on-the-job injuries per 10,000 employees. Round your answer to hundredths.

A)2.669 injuries per 10,000 employees
B)81.58 injuries per 10,000 employees
C)0.01 injury per 10,000 employees
D)0.008 injury per 10,000 employees

Question 63

Find the expected value.

-A 28-year-old man pays $57 for a one-year life insurance policy with coverage of $130,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy?

A)$21.00
B)-$56.97
C)$129,922.00
D)$78.00

Question 64

Use the data to find the required rate. Round your answer to thousandths unless indicated otherwise.

-A six mile strip of Sprinkle Road had 67 traffic fatalities last year. There were 2.6 million miles driven along this stretch. Determine the traffic fatality rate per 1,000,000 miles driven. Round your answer to hundredths.

A)25.77 deaths per 1,000,000 miles driven
B)25,769,230.77 deaths per 1,000,000 miles driven
C)2.57692308 deaths per 1,000,000 miles driven
D)0.04 death per 1,000,000 miles driven

Question 65

Answer the question about the Law of Large Numbers.

-A gambler playing blackjack in a casino has lost each of his first 16 bets. If he correctly understood the Law of large Numbers, which strategy would he use in betting on future blackjack hands?
A. He should bet based on the merit of each individual hand. While the proportion of wins should eventually approach
The true probability of winning, this does not mean that he is likely to recover early losses.
B. He should bet more on the next 16 hands, because the proportion of wins should quickly approach the true
Probability of winning.
B. He should bet less on the next 16 hands, because it doesn't look like this is a good day for him.
D. He shouldn't use any of the above strategies.

A)c
B)b
C)a
D)d

Question 66

Find the expected value.

-In a game, you have a $\frac { 1 } { 22 }$ probability of winning $89 and a $\frac { 21 } { 22 }$ Probability of losing $9. What is your expected
Value?

A)-$8.59
B)$12.64
C)$4.05
D)-$4.55

Question 67

Use the data to find the required rate. Round your answer to thousandths unless indicated otherwise.

-A six mile strip of Sprinkle Road had 50 traffic fatalities last year. There were 2.4 million miles driven along this stretch. Determine the traffic fatality rate per 100,000 miles driven. Round your answer to hundredths.

A)2.08 deaths per 100,000 miles driven
B)20.83 deaths per 100,000 miles driven
C)24 deaths per 100,000 miles driven
D)4800.00 deaths per 100,000 miles driven

Question 68

Answer the question about the Law of Large Numbers.

-John decides to play the state lotto, which requires the purchaser to select six numbers between 1 and 50. he selects 4, 4, 4, 4, 4, 4 for his numbers, believing that these are just as likely as any other series of six numbers between 1 and 50. He also notes that these numbers have not yet been selected as winning numbers. What can we accurately say about John's choice of numbers?
A. It is a reasonable choice.
B. It is an unreasonable choice, since a series of six 4s is very unlikely.
C. It is a reasonable choice, because these numbers are due to be picked.
D. It is a unreasonable choice, because these numbers have never been picked before.

A)d
B)a
C)b
D)c

Question 69

Use the data to find the required rate. Round your answer to thousandths unless indicated otherwise.

-At an intersection in Normal, Illinois, there were 90 vehicle accidents with 168,199 vehicles passing through the intersection. Determine the accident rate per 1000 vehicles.

A)0.00054 accident per 1000 vehicles
B)0.535 accident per 1000 vehicles
C)1,868,877.78 accidents per 1000 vehicles
D)168.199 accidents per 1000 vehicles

Question 70

Find the expected value.

-Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 10 minutes without delay. What is the expected value of your waiting time?

A)1 min
B)2 min
C)5 min
D)3 min

Question 71

Use the data to find the required rate. Round your answer to thousandths unless indicated otherwise.

-An insurance company reported that last year there were claims for medical expenses for 2629 on-the-job injuries. The company covers 329,507 employees. Find the rate of on-the-job injuries per 1000 employees. Round your answer to hundredths.

A)7.98 injuries per1000 employees
B)0.008 injury per 1000 employees.
C)0.13 injury per 1000 employees,
D)2.629 injuries per 1000 employees.

Question 72

Find the expected value.

-Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 1 or a 2, nothing otherwise. What is your expected value of your gain or loss?

A)$0.00
B)-$1.00
C)$3.00
D)$1.00

Question 73

Use the data to find the required rate. Round your answer to thousandths unless indicated otherwise.

-At an intersection in Normal, Illinois, there were 170 vehicle accidents with 255,872 vehicles passing through the intersection. Determine the accident rate per 10,000 vehicles.

A)6.644 accidents per 10,000 vehicles
B)255.872 accidents per 10,000 vehicles
C)1,505,129.41 accidents per 10,000 vehicles
D)0.00066 accident per 10,000 vehicles

Question 74

A family with four children is randomly selected. Assume that births of boys and girls are equally likely. Construct a table showing the probability distribution for the events 4 girls, 3 girls, 2 girls, 1 girl, and 0 girls..
$\quad$ $\quad$$\quad$$\text {4 Child Family }$
$\begin{array}{l}\begin{array} { l l c } \hline { \text { Result } } && \text { Probability } \\\hline \\ \\ \\ \\ \\\hline \text { Total } & & \end{array}\end{array}$

A)
$\quad$ $\quad$$\quad$$\text {4 Child Family }$
$\begin{array}{l}\begin{array} { l l c } \hline { \text { Result } } && \text { Probability } \\\hline 4 \text { girls } & 0 \text { boys } & 1 / 16 \\3 \text { girls } & 1 \text { boy } & 4 / 16 \\2 \text { girls } & 2 \text { boys } & 6 / 16 \\1 \text { girl } & 3 \text { boys } & 4 / 16 \\0 \text { girls } & 4 \text { boys } & 1 / 16 \\\hline \text { Total } & & 1\end{array}\end{array}$

B) $\quad$ $\quad$$\quad$$\text {4 Child Family }$
$\begin{array}{l}\begin{array} { l l c } \hline { \text { Result } } && \text { Probability } \\\hline 4 \text { girls } & 0 \text { boys } & 1 \\3 \text { girls } & 1 \text { boy } & 1 \\2 \text { girls } & 2 \text { boys } & 1 \\1 \text { girl } & 3 \text { boys } & 1 \\0 \text { girls } & 4 \text { boys } & 1 \\\hline \text { Total } && 5\end{array}\end{array}$

C)
$\quad$ $\quad$$\quad$$\text {4 Child Family }$
$\begin{array}{l}\begin{array} { l l c } \hline { \text { Result } } && \text { Probability } \\\hline 4 \text { girls } & 0 \text { boys } & 1 / 5 \\3 \text { girls } & 1 \text { boy } & 1 / 5 \\2 \text { girls } & 2 \text { boys } & 1 / 5 \\1 \text { girl } & 3 \text { boys } & 1 / 5 \\0 \text { girls } & 4 \text { boys } & 1 / 5\\\hline \text { Total } && 1\end{array}\end{array}$

D)
$\quad$ $\quad$$\quad$$\text {4 Child Family }$
$\begin{array}{l}\begin{array} { l l c } \hline { \text { Result } } && \text { Probability } \\\hline4 \text { girls } & 0 \text { boys } & 1 \\3 \text { girls } & 1 \text { boy } & 4 \\2 \text { girls } & 2 \text { boys } & 6 \\1 \text { girl } & 3 \text { boys } & 4 \\0 \text { girls } & 4 \text { boys } & 1\\\hline \text { Total } && 16\end{array}\end{array}$

Question 75

Find the expected value.

-Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $10,000. What is your expected value?

A)$90.00
B)$0.90
C)$9.00
D)-$0.90

Question 76

Answer the question about the Law of Large Numbers.
A fair coin is tossed 5000 times. What can you say about getting the outcome of exactly 2500 tails?
A. Since the probability of a tail is 0.5 for each toss, you should expect exactly 2500 tails in 5000 tosses.
B. You should not expect exactly 2500 tails in 5000 tosses, but the proportion of tails should approach 0.5 as the number
Of tosses increases.
C. You should expect between 2475 and 2525 tails in 5000 tosses.
D. Getting 2500 tails is no more likely than getting any other number of tails in 5000 tosses.

A)c
B)a
C)b
D)d

Question 77

Answer the question about the Law of Large Numbers.
Jim has been stopped for speeding three times in the last year, but each time was given a warning instead of a ticket.
What does it mean to say that "the law of averages will catch up with him"?
A. It means that average drivers receive tickets, not warnings, when stopped for speeding.
B. It means that Jim is "due" to receive a ticket next time he is stopped for speeding.
C. It means that, in the long run, Jim should not expect to be stopped for minor speeding violations.
D. None of the above is a correct interpretation.

A)b
B)a
C)d
D)c

Question 78

Answer the question about the Law of Large Numbers.
Melissa tosses a fair coin 4 times. What can we reasonably conclude about the outcome of 4 heads occurring?
A. It will occur exactly one time.
B. It will probably never occur, because it is an unusual outcome.
C. It will occur exactly 4 times.
D. None of the above is true.

A)a
B)c
C)d
D)b

Question 79

Use the data to find the required rate. Round your answer to thousandths unless indicated otherwise.

-At an intersection in Normal, Illinois, there were 83 vehicle accidents with 167,231 vehicles passing through the intersection. Determine the accident rate per 100 vehicles.

A)0.00050 accident per 100 vehicles
B)0.050 accident per 100 vehicles
C)1672.31 accidents per 100 vehicles
D)201,483.13 accidents per 100 vehicles

Question 80

Find the expected value.

-A contractor is considering a sale that promises a profit of $39,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such)of $3000 with a probability of 0.3. What is the expected profit?

A)$29,400
B)$36,000
C)$27,300
D)$26,400