AnswersConcepts in Probability and Statistics AConditional Probability

Conditional Probability — Unit test Answers

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In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red.If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?

A
One-eighth
Option A
B
One-half
Option B
C
Two-thirds
Option C
D
Three-fourths
Option D
2
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The cable company is analyzing the data from two satellite television providers to determine whether their users spend more time watching live television or shows that have been recorded.Satellite Company X: 89 live, 430 recordedSatellite Company Y: 65 live, 94 recorded

A
41%
B
59%
C
77%
D
83%
3

A random number generator is used to create a list of 300 single-digit numbers. Of those 300 numbers, 146 are odd and 154 are even. The number 8 was generated 22 times.What is the experimental probability of an even number other than 8 being generated? Write your answer as a decimal to the nearest hundredths place.

A
0.23
B
0.35
C
0.44
D
0.52
4

Eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag. Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag.Which shows subset A?

A
A = {6}
B
A = {1, 3, 5, 7}
C
A = {1, 2, 3, 4, 5, 7, 8}
D
A = {1, 2, 3, 4, 5, 6, 7, 8}
5

Which probabilities are correct? Select two options.

A
P(A|C) =
Option A
B
P(C|B) =
Option B
C
P(A) =
Option C
D
P(C) =
Option D
E
P(B|A) =
Option E
6

Pedro has determined that the probability his shot will score in a lacrosse game is 0.30.What is the probability that he will score on two consecutive shots?

A
0.09
B
0.15
C
0.30
D
0.60
7

Bart found 20 quadrilaterals in his classroom. He made a Venn diagram using the properties of the quadrilaterals, comparing those with four equal side lengths (E) and those with four right angles (R).

Question illustration
A
25%
B
33%
C
40%
D
67%
8

James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The results are shown below.Bring lunch: 46 males, 254 femalesBuy lunch: 176 males, 264 females

A
P(buys lunch | male) = P(male) = 0.4.
B
P(male | buys lunch) = P(male) = 0.3.
C
P(buys lunch | male) = 0.3 and P(male) = 0.4.
D
P(male | buys lunch) = 0.4 and P(male) = 0.3.
9

Which events are mutually exclusive? Select two options.

A
landing on a shaded portion and landing on an even number
B
landing on a shaded portion and landing on a number greater than 3
C
landing on a shaded portion and landing on a 3
D
landing on an unshaded portion and landing on an odd number
E
landing on an unshaded portion and landing on a number less than 2
10

Christina is randomly choosing three movies to take on vacation from nine action movies, seven science fiction movies, and four comedies. Which statement is true?

A
The probability that Christina will choose three comedies can be expressed as .
Option A
B
The probability that Christina will choose three action movies can be expressed as .
Option B
C
The probability that Christina will not choose all comedies can be expressed as 1 − .
Option C
D
The probability that Christina will not choose all action movies can be expressed as 1 − .
Option D
11

A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive.What is true about spinning the spinner one time? Select three options.S = {1, 2, 3, 4, 5, 6, 7, 8}If A is a subset of S, A could be {1, 2, 3}.If A is a subset of S, A could be {7, 8, 9}.If a subset A represents spinning a number less than 4,then A = {1, 2, 3, 4}.If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.

A
S = {1, 2, 3, 4, 5, 6, 7, 8}
B
If A is a subset of S, A could be {1, 2, 3}.
C
If A is a subset of S, A could be {7, 8, 9}.
D
If a subset A represents spinning a number less than 4,then A = {1, 2, 3, 4}.
E
If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.
12

The spinner is equally likely to land on any of the six sections.

Question illustration
A
Two-ninths
Option A
B
One-half
Option B
C
Two-thirds
Option C
D
Five-sixths
Option D
13

The table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have.

Question illustration
A
65%
B
70%
C
75%
D
80%
14

The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1.Why are the events not independent?

A
The sum of P(A) and P(B) is greater than P(A and B).
B
The product of P(A) and P(B) is greater than P(A and B).
C
The product of P(A) and P(B) is not equal to P(A and B).
D
The sum of P(A) and P(B) is not equal to P(A and B).
15

Which statements are true about Yuri’s experiment? Select three options.

A
The theoretical probability of spinning any one of the five colors is 20%.
B
The experimental probability of spinning blue is .
Option B
C
The theoretical probability of spinning green is equal to the experimental probability of spinning green.
D
The experimental probability of spinning yellow is less than the theoretical probability of spinning yellow.
E
If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
16

When a softball player gets a hit, it can be a single, double, triple, or home run. When Josephine is at bat, the probability that she hits a single is 15 percent and the probability that she hits a double is 5 percent.What is the probability that Josephine hits a single or a double when she is at bat?

A
3 percent
B
10 percent
C
20 percent
D
75 percent
17

A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday’s lunch.What is the theoretical probability that applesauce and broccoli will both be offered on Monday?

A
10%
B
20%
C
50%
D
80%
18

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order.What is the sample space showing the possible orders of the other three runners?

A
S = {FGI, GFI, IFG}
B
S = {FGI, FIG, GFI, GIF}
C
S = {FGI, FIG, GFI, GIF, IFG, IGF}
D
S = {FGI, FIG, GFI, GIF, HFG, HGI, IFG, IGF}
19

Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking.What subset of the sample space, A, represents the complement of the event in which Joe plays in the first match?

A
A = {KL}
B
A = {KJ, KL}
C
A = {KL, LK}
D
A = {KJ, KL, LJ}
20

If events A and B are independent, and the probability that event A occurs is 83%, what must be true?

A
The probability that event B occurs is 17%.
B
The probability that event B occurs is 83%.
C
The probability that event A occurs, given that event B occurs, is 83%.
D
The probability that event B occurs, given that event A occurs, is 83%.

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