Question 1

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 two tails?

Accepted Answer

The answer of If you flip a coin three times,...

Question 2

A study of two types of weed killers was done on two identical weed plots. One weed killer killed 15% more weeds than the other. This difference was significant at the 0.05 level. What Does this mean?
A) The improvement was due to the fact that there were more weeds in one study.
B) The probability that the difference was due to chance alone is greater than 0.05.
C) The probability that one weed killer performed better by chance alone is less than 0.05.
D) There is not enough information to make any conclusion.

Accepted Answer

The statement means that the likelihood of the observed difference in weed-killing effectiveness being due to random chance is less than 5%, indicating a statistically significant result.

Question 3

A class consists of 50 women and 82 men. If a student is randomly selected, what is the probability that the student is a woman?

Accepted Answer

The answer of A class consists of 50 women and...

Question 4

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event).
-Rolling a 4 with a fair die
A) Outcome
B) Event

Accepted Answer

The answer of state whether there is one way for...

Question 5

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 transportation results. If one of the 100 employees is randomly selected, find the probability that the person does not commute by public transportation.  
A) Public transportation: 7 full-time, 8 part-time
B) Bicycle: 3 full-time, 4 part-time
C) Drive alone: 29 full-time, 34 part-time
D) Carpool: 9 full-time, 6 part-time

Accepted Answer

The answer of 100 employees of a company are asked...

Question 6

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event).
-Drawing three queens from a regular deck of cards
A) Outcome
B) Event

Accepted Answer

Drawing three queens from a deck of cards can occur in multiple ways, as there are four queens in the deck and different combinations of three queens can be drawn.

Question 7

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event).
-Tossing one head with a penny followed by one tail with a dime
A) Outcome
B) Event

Accepted Answer

The answer of state whether there is one way for...

Question 8

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 no chocolate bar was eaten.

Accepted Answer

The answer of Sammy and Sally each carry a bag...

Question 9

Of 1308 people who came into a blood bank to give blood, 314 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure (to 3 decimal places).

Accepted Answer

The answer of Of 1308 people who came into a...

Question 10

From the table in Problem 16, how many 60-year old females on average will be living at age 61?

Accepted Answer

The answer of From the table in Problem 16, how...

Question 11

In the first series of rolls of a die, the number of odd numbers exceeded the number of even numbers by 5. In the second series of rolls of the same die, the number of odd numbers exceeded the number of even numbers by 11. Determine which series is closer to the 50/50 ratio of odd/even expected of a fairly rolled die.
A) The second series is closer because the difference between odd and even numbers is greater than the difference for the first series.
B) The first series is closer because the difference between odd and even numbers is less than the difference for the second series.
C) Since $1 / 2 > 1 / 5 > 1 / 11$ , the first series is closer.
D) The series closer to the theoretical 50/50 cannot be determined unless the total number of rolls for both series is given.

Accepted Answer

Without knowing the total number of rolls in each series, we cannot determine which series is closer to the 50/50 ratio.

Question 12

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?

Accepted Answer

The answer of If you flip a coin three times,...

Question 13

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 $500. What is your expected value?
A) $0.00
B) −$0.40
C) −$1.00
D) −$0.50

Accepted Answer

The answer of Suppose you buy 1 ticket for $1...

Question 14

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event).
-Tossing two tails with two fair coins
A) Outcome
B) Event

Accepted Answer

The answer of state whether there is one way for...

Question 15

The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number living out of an original 100,000, and the additional life expectancy for a person of that age.
Exact Male Female P(Death Additional P(Death Additional Age 
\(\begin{array}{c}
\quad\quad\quad\text { Male }  \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Female }\
\begin{array}{|c|c|c|c|c|c|c|}
\hline{\text {Exact  Age }} & \begin{array}{c}
\text { P(Death } \
\text { within one } \
\text { year) }
\end{array} & \begin{array}{c}
\text { Number of } \
\text { Living }
\end{array} & \begin{array}{c}
\text { Additional } \
\text { Life } \
\text { Expectancy }
\end{array} & \begin{array}{c}
\text { P(Death } \
\text { within one } \
\text { year) }
\end{array} & \begin{array}{c}
\text { Number of } \
\text { Living }
\end{array} & \begin{array}{c}
\text { Additional } \
\text { Life } \
\text { Expectancy }
\end{array} \
\hline 10 & 0.000111 & 99,021 & 65.13 & 0.000105 & 99,217 & 70.22 \
\hline 20 & 0.001287 & 98,451 & 55.46 & 0.000469 & 98,950 & 60.40 \
\hline 30 & 0.001375 & 97,113 & 46.16 & 0.000627 & 98,431 & 50.69 \
\hline 40 & 0.002542 & 95,427 & 36.88 & 0.001498 & 97,513 & 41.11 \
\hline 50 & 0.005696 & 91,853 & 28.09 & 0.003240 & 95,378 & 31.91 \
\hline 60 & 0.012263 & 84,692 & 20.00 & 0.007740 & 90,847 & 23.21 \
\hline 70 & 0.028904 & 70,214 & 12.98 & 0.018938 & 80,583 & 15.45 \
\hline 80 & 0.071687 & 44,272 & 7.43 & 0.049527 & 59,341 & 9.00 \
\hline 90 & 0.188644 & 12,868 & 3.68 & 0.146696 & 24,331 & 4.45 \
\hline
\end{array}\end{array}\) To what age may a male of age 50 expect to live on the average?

Accepted Answer

The answer of The following table is from the Social...

Question 16

Wisconsin has 72 counties. The names of six of them begin with the letter C. Is it "significant" for a randomly chosen Wisconsin county to be one of those six counties.

Accepted Answer

The probability of randomly choosing one of the six counties that begin with "C" is 6/72, which is approximately 8.33%. This is not considered statistically significant.

Question 17

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?

Accepted Answer

The answer of On a multiple choice test, each question...

Question 18

If you are told that a mystery person's birthday is in February, would it be "significant" to
guess that person's birth date (not including the year).

Accepted Answer

There are only 28 or 29 days in February, so it is more likely to guess the correct birth date compared to other months with 30 or 31 days.

Question 19

The probability that Luis will pass his statistics test is 0.94. Find the probability that he will fail his statistics test.

Accepted Answer

The answer of The probability that Luis will pass his...

Question 20

Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?

Accepted Answer

The answer of Suppose you have an extremely unfair die:...

Quiz 6: Probability in Statistics

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 two tails?

A study of two types of weed killers was done on two identical weed plots. One weed killer killed 15% more weeds than the other. This difference was significant at the 0.05 level. What Does this mean?

A class consists of 50 women and 82 men. If a student is randomly selected, what is the probability that the student is a woman?

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event) . -Rolling a 4 with a fair die

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event) . -Drawing three queens from a regular deck of cards

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event) . -Tossing one head with a penny followed by one tail with a dime

Of 1308 people who came into a blood bank to give blood, 314 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure (to 3 decimal places).

From the table in Problem 16, how many 60-year old females on average will be living at age 61?

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?

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 $500. What is your expected value?

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event) . -Tossing two tails with two fair coins

Wisconsin has 72 counties. The names of six of them begin with the letter C. Is it "significant" for a randomly chosen Wisconsin county to be one of those six counties.

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?

If you are told that a mystery person's birthday is in February, would it be "significant" to guess that person's birth date (not including the year).

The probability that Luis will pass his statistics test is 0.94. Find the probability that he will fail his statistics test.

Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?