Question 1

Determine whether the events are disjoint.
-Get stung by a bee. 
Get stung by a wasp.

A) Yes
B) No

Accepted Answer

The events are not disjoint because it is possible for both events to occur simultaneously; a person can be stung by both a bee and a wasp.

Question 2

The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. $$\begin{array}{l}

\begin{array} { r | r } \text { Waiting Time } & \text {Number of }\
\text { (minutes) } & \text { Customers } \
\hline 0 - 3 & 11 \
4 - 7 & 14 \
8 - 11 & 12 \
12 - 15 & 8 \
16 - 19 & 4 \
20 - 23 & 3 \
24 - 27 & 2
\end{array}
\end{array}$$ 
If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes?
A) 0.741
B) 0.685
C) 0.537
D) 0.148

Accepted Answer

The answer of The manager of a bank recorded the...

Question 3

Find the indicated probability. Round to the nearest thousandth.
-A study conducted at a certain college shows that 56% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
A) 0.993
B) 0.560
C) 0.167
D) 0.969

Accepted Answer

The probability that at least one graduate finds a job is 1 minus the probability that none of the graduates find a job. The probability that a single graduate does not find a job is 0.44 (1 - 0.56). For 6 graduates, this probability is 0.44^6. Subtracting this from 1 gives approximately 0.993.

Question 4

Find the indicated probability.
-A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9).

A) 10

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

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

D) $\frac { 5 } { 13 }$

Accepted Answer

The answer of Find the indicated probability.
-A card is drawn...

Question 5

Determine whether the events are disjoint.
-Find a ten dollar bill on the sidewalk. 
Find a ten dollar bill on the grass.
A) Yes
B) No

Accepted Answer

The answer of Determine whether the events are disjoint.
-Find a...

Question 6

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. $\begin{array}{llcc}
0&1&1&2&2&0&1&1&2&3&2&1&2&1&2&2&1&2&3&1&2&2&2&0&3&1&0&2&1&2&1
\end{array}$

Estimate the probability that sales will rise at least moderately.
A) 0.452
B) 0.516
C) 0.613
D) 0.512

Accepted Answer

The probability that sales will rise at least moderately (i.e., values of 2 or 3) is calculated by counting the number of 2s and 3s and dividing by the total number of observations. There are 16 occurrences of 2 and 3 out of 31 total observations, giving a probability of 16/31 ≈ 0.516.

Question 7

Find the indicated probability. Round to the nearest thousandth.
-In a batch of 8,000 clock radios 7% are defective. A sample of 5 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected?
A) 0.200
B) 0.696
C) 0.0700
D) 0.304

Accepted Answer

The probability that the entire batch will be rejected is the complement of the probability that none of the 5 selected radios are defective. The probability that a single radio is not defective is 0.93. The probability that all 5 radios are not defective is (0.93)^5. Therefore, the probability that at least one is defective is 1 - (0.93)^5 = 0.304.

Question 8

The data set represents the income levels of the members of a country club. Find the probability that a randomly selected member earns at least $90,000. Round your answers to the nearest tenth. $$\begin{array} { r r r r r r r r r r } 
96,000 & 102,000 & 88,000 & 105,000 & 89,000 & 96,000 & 90,000 & 86,000 & 111,000 & 126,000 \
87,000 & 93,000 & 108,000 & 89,000 & 102,000 & 99,000 & 90,000 & 114,000 & 85,000 & 99,000
\end{array}$$
A) 0.4
B) 0.7
C) 0.6
D) 0.8

Accepted Answer

The answer of The data set represents the income levels...

Question 9

Find the indicated probability. Round to the nearest thousandth.
-An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one correct answer.
A) 0.900
B) 0.100
C) 0.999
D) 0.001

Accepted Answer

The probability of getting at least one correct answer is 1 minus the probability of getting all answers wrong. The probability of getting one answer wrong is 0.5, so for ten questions, it's 0.5^10. Subtract this from 1 to get approximately 0.999.

Question 10

Determine whether the events are disjoint.
-Get a full time day job as a teller with a bank. 
Get a full time day job as a cashier at a store.
A) Yes
B) No

Accepted Answer

The events are disjoint because it is not possible to have both a full time day job as a teller with a bank and a full time day job as a cashier at a store at the same time. Therefore, choosing one event eliminates the possibility of the other event occurring.

Question 11

Determine whether the events are disjoint.
-Draw one ball colored red from a bag. Draw one ball colored blue from the same bag.
A) Yes
B) No

Accepted Answer

The events are disjoint because you cannot draw a ball that is both red and blue at the same time. Therefore, the events are mutually exclusive.

Question 12

In a certain class of students, there are 8 boys from Wilmette, 3 girls from Kenilworth, 6 girls from Wilmette, 6 boys from Glencoe, 5 boys from Kenilworth and 3 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) 0.32
B) 0.263
C) 0.097
D) 0.258

Accepted Answer

The answer of In a certain class of students, there...

Question 13

From the information provided, create the sample space of possible outcomes.
-Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten?
A) LD-CD LD-CD LD-CD LD-LP LD-LP LD-LP CD-LP CD-LP CD-LP
B) LD-LD CD-LD LP-LP LD-LP CD-CD LD-LP LP-CD CD-LD LP-LD
C) LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD CD-LP LP-LD
D) CD-LD LD-LP LP-CD LP-LP LD-LD

Accepted Answer

The sample space includes all combinations of candies Fred and Ed can eat: LD-LD, CD-LD, LP-LP, LD-CD, CD-CD, LD-LP, LP-CD, CD-LP, LP-LD.

Question 14

A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?

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

B) $\frac { 2 } { 3 }$

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

D) 12

Accepted Answer

The answer of A spinner has equal regions numbered 1...

Question 15

A study of consumer smoking habits includes 162 people in the 18-22 age bracket (57 of whom smoke), 127 people in the 23-30 age bracket (37 of whom smoke), and 85 people in the 31-40 age bracket (20 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes.
A) 0.545
B) 0.644
C) 0.291
D) 0.099

Accepted Answer

The probability of getting someone who is age 23-30 is 127/374 = 0.3396. The probability of getting someone who smokes is 114/374 = 0.3048. The probability of getting someone who is age 23-30 or smokes is 0.3396 + 0.3048 - 0.0348 = 0.61.

Question 16

Evaluate the expression
-$ { }_{8} C_{4} $

A) 2
B) 24
C) 70
D) 420

Accepted Answer

The answer of Evaluate the expression
-$ { }_{8} C_{4} $

A)...

Question 17

Find the indicated probability.
-Among the contestants in a competition are 46 women and 20 men. If 5 winners are randomly selected, what is the probability that they are all men? Round to five decimal places.
A) 0.01554
B) 0.01131
C) 0.16446
D) 0.00173

Accepted Answer

The probability that all 5 winners are men is calculated by dividing the number of ways to choose 5 men from 20 by the number of ways to choose 5 people from 66 (46 women + 20 men). This is (20 choose 5) / (66 choose 5), which equals approximately 0.00173.

Question 18

Determine whether the events are disjoint.
-Meet a man with an umbrella. 
Meet a man with a raincoat.

A) Yes
B) No

Accepted Answer

The events are not mutually exclusive because it is possible to meet a man who is wearing both an umbrella and a raincoat at the same time.

Question 19

In a homicide case 8 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 8 witnesses would pick the same person.
A) 0.0000305
B) 0.0000026
C) 1.6
D) 0.0000128

Accepted Answer

The answer of In a homicide case 8 different witnesses...

Question 20

Use Bayes' theorem to find the indicated probability.
-Pierre has three coins one of which is biased so that it turns up tails 80% of the time. If he randomly selects one of the coins, tosses it three times, and obtains three tails, what is the probability that this is the biased coin?
A) 0.512
B) 0.739
C) 0.672
D) 0.333

Accepted Answer

The answer of Use Bayes' theorem to find the indicated...

Quiz 4: Probability

Determine whether the events are disjoint. -Get stung by a bee. Get stung by a wasp.

Find the indicated probability. -A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9) .

Determine whether the events are disjoint. -Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass.

Find the indicated probability. Round to the nearest thousandth. -An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one correct answer.

Determine whether the events are disjoint. -Get a full time day job as a teller with a bank. Get a full time day job as a cashier at a store.

Determine whether the events are disjoint. -Draw one ball colored red from a bag. Draw one ball colored blue from the same bag.

From the information provided, create the sample space of possible outcomes. -Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten?

A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?

Evaluate the expression - ${ }_{8} C_{4}$

Find the indicated probability. -Among the contestants in a competition are 46 women and 20 men. If 5 winners are randomly selected, what is the probability that they are all men? Round to five decimal places.

Determine whether the events are disjoint. -Meet a man with an umbrella. Meet a man with a raincoat.

In a homicide case 8 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 8 witnesses would pick the same person.

Use Bayes' theorem to find the indicated probability. -Pierre has three coins one of which is biased so that it turns up tails 80% of the time. If he randomly selects one of the coins, tosses it three times, and obtains three tails, what is the probability that this is the biased coin?

Quiz 4: Probability

Determine whether the events are disjoint. -Get stung by a bee. Get stung by a wasp.

Find the indicated probability. -A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9) .

Determine whether the events are disjoint. -Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass.

Find the indicated probability. Round to the nearest thousandth. -An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one correct answer.

Determine whether the events are disjoint. -Get a full time day job as a teller with a bank. Get a full time day job as a cashier at a store.

Determine whether the events are disjoint. -Draw one ball colored red from a bag. Draw one ball colored blue from the same bag.

From the information provided, create the sample space of possible outcomes. -Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten?

A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?

Evaluate the expression - 8C4 { }_{8} C_{4} 8​C4​

Find the indicated probability. -Among the contestants in a competition are 46 women and 20 men. If 5 winners are randomly selected, what is the probability that they are all men? Round to five decimal places.

Determine whether the events are disjoint. -Meet a man with an umbrella. Meet a man with a raincoat.

In a homicide case 8 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 8 witnesses would pick the same person.

Use Bayes' theorem to find the indicated probability. -Pierre has three coins one of which is biased so that it turns up tails 80% of the time. If he randomly selects one of the coins, tosses it three times, and obtains three tails, what is the probability that this is the biased coin?

Evaluate the expression - ${ }_{8} C_{4}$