Question 1

Find the indicated probability.
-The probability that an event will occur is 0.2. What is the probability that the event will not occur?

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

B) $0.8$

C) 0

D) None of the above is correct.

Accepted Answer

The probability that an event will not occur is 1 minus the probability that it will occur. Therefore, 1 - 0.2 = 0.8.

Question 2

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
-The table below describes the smoking habits of a group of asthma sufferers.
 $\begin{array}{r|crrr} 
& &\text { Light } & \text { Heavy } \
& \text { Nonsmoker } & \text { smoker } & \text { smoker } & \text { Total } \
\hline \text { Men } & 358 & 71 & 69 & 498 \
\text { Women } & 304 & 78 & 76 & 458 \
\text { Total } & 662 & 149 & 145 & 956
\end{array}$

If one of the 956 subjects is randomly selected, find the probability that the person chosen is a nonsmoker given that it is a woman. Round to the nearest thousandth.
A) 0.459
B) 0.379
C) 0.318
D) 0.664

Accepted Answer

The answer of Find the indicated probability. Express your answer...

Question 3

Provide a written description of the complement of the given event.
-Of the thirteen different women Calvin asks for a date, at least one of them accepts.
A) At most one of the women accepts Calvin's offer.
B) None of the women accept Calvin's offer.
C) All but one woman accepts Calvin's offer.
D) All of the women accept Calvin's offer.

Accepted Answer

The complement of "at least one of them accepts" is "none of them accept."

Question 4

Express the indicated degree of likelihood as a probability value.
-"You cannot determine the exact decimal-number value of $\pi . "$
A) 0
B) 1
C) $3.14$
D) $0.5$

Accepted Answer

The statement "You cannot determine the exact decimal-number value of $\pi . "$ is a certainty, so the probability is 1.

Question 5

A firm uses trend projection and seasonal factors to simulate sales for a given time period. It assigns "0" if sales fall, "1" if sales are steady, "2" if sales rise moderately, and "3" if sales rise a lot.
The simulator generates the following output. $\begin{array}{llcc}
0&1&1&2&0&0&1&1&0&3&2&1&0&1&0&2&1&2&3&1&2&0&2&0&3&1&0&2&1&0&1
\end{array}$

Estimate the probability that sales will remain steady.
A) 0.412
B) 0.125
C) 0.419
D) 0.355

Accepted Answer

The answer of A firm uses trend projection and seasonal...

Question 6

Evaluate the expression.

-$\frac { 10 ! } { 4 ! }$

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

B) 40,000

C) 151,200

D) 2 !

Accepted Answer

The expression $\frac { 10 ! } { 4 ! }$ simplifies to $\frac { 10 \times 9 \times 8 \times 7 \times 6 \times 5 }{ 1 }$, which equals 151,200.

Question 7

Is Event B dependent or independent of Event A?
-A: A Chicagoan visits New York on vacation. 
B: He visits Central Park.

A) Dependent
B) Independent

Accepted Answer

Event B (visiting Central Park) is dependent on Event A (visiting New York on vacation) because the individual must first visit New York in order to visit Central Park.

Question 8

Find the indicated probability.
-A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4).

A) $\frac { 4 } { 13 }$

B) $\frac { 12 } { 13 }$

C) 16

D) $\frac { 2 } { 13 }$

Accepted Answer

There are 12 face cards and 4 cards of 4s in a deck. However, one of the 4s is also a face card, so we have 12 + 3 = 15 unique cards. The probability is 15/52, which simplifies to 4/13.

Question 9

Find the indicated complement.
-Find $\mathrm { P } ( \overline { \mathrm { A } } )$, given that $\mathrm { P } ( \mathrm { A } ) = 0.956$.
A) $1.046$
B) 0
C) $0.044$
D) $1.956$

Accepted Answer

The complement of an event A is calculated as $1 - \mathrm{P}(A)$. Therefore, $\mathrm{P}(\overline{\mathrm{A}}) = 1 - 0.956 = 0.044$.

Question 10

In one town, 78% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary.
A) 3.12
B) 0.37
C) 0.051
D) 0.78

Accepted Answer

The answer of In one town, 78% of adults have...

Question 11

What is the probability that 4 randomly selected people all have different birthdays? Round to four decimal places.
A) 0.9891
B) 0.9918
C) 0.9836
D) 0.9729

Accepted Answer

The probability that two randomly selected people have different birthdays is 364/365 (assuming no leap year). Therefore, the probability that four randomly selected people all have different birthdays is:
(364/365) x (363/365) x (362/365) = 0.9836 (rounded to four decimal places). Therefore, the correct choice is C.

Question 12

Find the indicated probability.
-A study of consumer smoking habits includes 159 people in the $18 - 22$ age bracket ( 48 of whom smoke), 132 people in the 23-30 age bracket (35 of whom smoke), and 94 people in the 31-40 age bracket ( 26 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age $18 - 22$ or does not smoke.
A) 1.13
B) 0.698
C) 0.288
D) 0.842

Accepted Answer

The probability of selecting someone who is age 18-22 or does not smoke is calculated by adding the probability of selecting someone age 18-22 and the probability of selecting someone who does not smoke, then subtracting the probability of selecting someone who is both age 18-22 and smokes. This results in (159/385) + (276/385) - (48/385) = 0.842.

Question 13

Estimate the probability of the event.
-Of 1950 people who came into a blood bank to give blood, 339 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.
A) 0.225
B) 0.174
C) 0.142
D) 0.093

Accepted Answer

The probability is estimated by dividing the number of people with high blood pressure by the total number of people. So, 339/1950 = 0.174.

Question 14

A bag contains 2 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

A) $\frac { 1 } { 7 }$

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

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

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

Accepted Answer

The answer of A bag contains 2 red marbles, 3...

Question 15

On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess? 
A) 1

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

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

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

Accepted Answer

When guessing randomly, each of the four answers has an equal chance of being chosen, so the probability of selecting the correct answer is 1 out of 4, or $\frac{1}{4}$.

Question 16

If an apple is hanging from a string and three flies land on it, find the probability that all three are on points that are within the same hemisphere.
A) 0.25
B) 0.125
C) 4
D) 0.333

Accepted Answer

There are 2 hemispheres, so the probability that the first fly lands on the same hemisphere as the apple is 1/2. The probability that the second fly lands on the same hemisphere as the apple and the first fly is 1/2, and the probability that the third fly lands on the same hemisphere as the apple, the first fly, and the second fly is 1/2. So the probability that all three flies land on the same hemisphere is (1/2) * (1/2) * (1/2) = 1/8 = 0.125.

Question 17

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
-Is it "unusual" to get 5 when a pair of dice is rolled?
A) Yes
B) No

Accepted Answer

The probability of rolling a sum of 5 with two dice is 4/36 or approximately 0.111, which is greater than 0.05, so it is not considered unusual.

Question 18

8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected? 
A) $\frac { 8 } { 27 }$

B) $\frac { 1 } { 2,220,075 }$

C) $\frac { 1 } { 40,320 }$

D) $\frac { 1 } { 213,127,200 }$

Accepted Answer

The probability of selecting the 8 tallest players from a list of 27 players is 1 / 2,220,075. This is because there are 27C8 ways to select 8 players from a list of 27 players, and only 1 of these ways will result in the 8 tallest players being selected.

Question 19

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
-The following table contains data from a study of two airlines which fly to Small Town, USA. $$\begin{array} { c | c c } 
&   \text { Number of flights} & \text { Number of flights }  \
& \text { which were on time } & \text { which were late } \
\hline \text { Podunk Airlines } & 33 & 6 \
\text { Upstate Airlines } & 43 & 5
\end{array}$$ 
If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight given that it was late. 
A) $\frac { 5 } { 87 }$

B) $\frac { 5 } { 48 }$

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

D) None of the above is correct.

Accepted Answer

The probability that a flight is an Upstate Airlines flight given that it was late is calculated by dividing the number of late Upstate Airlines flights by the total number of late flights: $ \frac{5}{11} $.

Question 20

Use Bayes' theorem to find the indicated probability.
-A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. It buys 24% of the connectors from supplier A, 36% from supplier B, and 40% from supplier C.
It finds that 2% of the connectors from supplier A are defective, 4% of the connectors from supplier B are defective, and 5% of the connectors from supplier C are defective.
If a customer buys one of these components and finds that the connector is defective, what is the probability that it came from supplier B?
A) 0.122
B) 0.04
C) 0.367
D) 0.581

Accepted Answer

Using Bayes' theorem, the probability that a defective connector came from supplier B is calculated as follows: P(B|D) = [P(D|B) * P(B)] / P(D). P(D|B) = 0.04, P(B) = 0.36, and P(D) = (0.02*0.24) + (0.04*0.36) + (0.05*0.40) = 0.0384. Thus, P(B|D) = (0.04*0.36) / 0.0384 = 0.367.

Quiz 4: Probability

Find the indicated probability. -The probability that an event will occur is 0.2. What is the probability that the event will not occur?

Provide a written description of the complement of the given event. -Of the thirteen different women Calvin asks for a date, at least one of them accepts.

Express the indicated degree of likelihood as a probability value. -"You cannot determine the exact decimal-number value of $\pi . "$

Evaluate the expression. - $\frac { 10 ! } { 4 ! }$

Is Event B dependent or independent of Event A? -A: A Chicagoan visits New York on vacation. B: He visits Central Park.

Find the indicated probability. -A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4) .

Find the indicated complement. -Find $\mathrm { P } ( \overline { \mathrm { A } } )$ , given that $\mathrm { P } ( \mathrm { A } ) = 0.956$ .

In one town, 78% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary.

What is the probability that 4 randomly selected people all have different birthdays? Round to four decimal places.

Estimate the probability of the event. -Of 1950 people who came into a blood bank to give blood, 339 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

A bag contains 2 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess?

If an apple is hanging from a string and three flies land on it, find the probability that all three are on points that are within the same hemisphere.

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -Is it "unusual" to get 5 when a pair of dice is rolled?

8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?

Quiz 4: Probability

Find the indicated probability. -The probability that an event will occur is 0.2. What is the probability that the event will not occur?

Provide a written description of the complement of the given event. -Of the thirteen different women Calvin asks for a date, at least one of them accepts.

Express the indicated degree of likelihood as a probability value. -"You cannot determine the exact decimal-number value of π."\pi . "π."

Evaluate the expression. - 10!4!\frac { 10 ! } { 4 ! }4!10!​

Is Event B dependent or independent of Event A? -A: A Chicagoan visits New York on vacation. B: He visits Central Park.

Find the indicated probability. -A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4) .

Find the indicated complement. -Find P(A‾) \mathrm { P } ( \overline { \mathrm { A } } ) P(A) , given that P(A) =0.956\mathrm { P } ( \mathrm { A } ) = 0.956P(A) =0.956 .

In one town, 78% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary.

What is the probability that 4 randomly selected people all have different birthdays? Round to four decimal places.

Estimate the probability of the event. -Of 1950 people who came into a blood bank to give blood, 339 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

A bag contains 2 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess?

If an apple is hanging from a string and three flies land on it, find the probability that all three are on points that are within the same hemisphere.

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -Is it "unusual" to get 5 when a pair of dice is rolled?

8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?

Express the indicated degree of likelihood as a probability value. -"You cannot determine the exact decimal-number value of $\pi . "$

Evaluate the expression. - $\frac { 10 ! } { 4 ! }$

Find the indicated complement. -Find $\mathrm { P } ( \overline { \mathrm { A } } )$ , given that $\mathrm { P } ( \mathrm { A } ) = 0.956$ .