Deck 8: Probability

Question 1

A bag contains 5 red marbles, 2 blue marbles, and 4 green marbles. What is the probability of choosing a blue marble?

A) P(B) =
B) P(B) =
C) P(B) =
D) P(B) =

Answer 1

P(B) =

Question 2

A lottery game contains 28 balls numbered 1 through 28. What is the probability of choosing a ball numbered 28, P(28)?

A) P(28) =
B) P(28) = 28
C) P(28) = 1
D) P(28) = 0

Answer 2

P(28) =

Question 3

Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 5, P(sum of 5)?

A) P(sum of 5) =
B) P(sum of 5) =
C) P(sum of 5) =
D) P(sum of 5) = 4

Answer 3

P(sum of 5) =

Question 4

A packet of sour worms contains four strawberry, four lime, two black currant, two orange sour, and three green apples worms. What is the probability that Dustin will choose a green apple sour worm, P(green apple)?

A) P(green apple) =
B) P(green apple) =
C) P(green apple) =
D) P(green apple) = 0

Question 5

A packet of sour worms contains four strawberry, four lime, two black currant, two orange sour, and three green apples worms. What is the probability that Dylan will not choose a green apple sour worm, P(not green apple)?

A) P(not green apple) = 0
B) P(not green apple) =
C) P(not green apple) =
D) P(not green apple) =

Question 6

A 6-sided die is rolled. What is the probability of rolling a number less than 2?

A)
B)
C)
D)

Question 7

A bag contains 6 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue?

A)
B)
C) 7
D)

Question 8

A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a ball that has an even number?

A)
B)
C)
D) 7

Question 9

Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 9?

A)
B)
C) 6
D)

Question 10

A sample space consists of 118 separate events that are equally likely. What is the probability of each?

A) 0
B)
C) 118
D) 1

Question 11

Find the probability of correctly answering the first 5 questions on a multiple choice test if random guesses are made and each question has 4 possible answers.

A)
B)
C)
D)

Question 12

Find the indicated probability:

-In a family with family with 4 children, excluding multiple births, what is the probability of having 2 girls and 2 boys, in that order? Assume that a boy is as likely as a girl at each birth.

A)
B)
C)
D)

Question 13

Find the probability:

-A single fair die is rolled. The number on the die is a 3 or a 5.

A)
B)
C)
D) 2

Question 14

Find the probability:

-A lottery game has balls numbered 1 through 21. A randomly selected ball has an even number or a 10.

A)
B) 10
C)
D)

Question 15

Find the probability:

-The table below describes the smoking habits of a group of asthma sufferers. If one of the 1124 people is randomly selected, find the probability that the person is a man or a heavy smoker.

A) 0.512
B) 0.552
C) 0.511
D) 0.471

Question 16

Find the probability:

-A study conducted at a certain college shows that 62% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

A) 0.200
B) 0.908
C) 0.992
D) 0.620

Question 17

Find the probability:

-A sample of 4 different calculators is randomly selected from a group containing 14 that are defective and 26 that have no defects. What is the probability that at least one of the calculators is defective?

A) 0.140
B) 0.164
C) 0.836
D) 0.821

Question 18

Find the probability:

-In a batch of 8,000 clock radios 6% are defective. A sample of 11 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) 0.0909
B) 0.506
C) 0.494
D) 0.0600

Question 19

In a survey of the number of DVDs in a house, the table shows the probabilities.

-Find the probability of a house having 1 or 2 DVDs.

A) 0.83
B) 0.38
C) 0.57
D) 0.95

Question 20

In a survey of the number of DVDs in a house, the table shows the probabilities.

-Find the probability of a house having 3 or more DVDs.

A) 0.05
B) 0.57
C) 0.38
D) 0.83

Question 21

In a survey of the number of DVDs in a house, the table shows the probabilities.

-Find the probability of a house having fewer than 2 DVDs.

A) 0.29
B) 0.57
C) 0.71
D) 0.38

Question 22

Estimate the indicated probability:

-College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. A randomly selected student prefers a cheese topping.

A) . 321
B) . 109
C) . 338
D) . 339

Question 23

Estimate the indicated probability:

-College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. A randomly selected student who is a a junior or senior is also prefers veggie. Round the answer to the nearest hundredth.

A) . 212
B) . 638
C) . 386
D) . 375

Question 24

Estimate the indicated probability:

-College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. A randomly selected student prefers a cheese topping.

A) . 172
B) .0 54
C) . 569
D) . 314

Question 25

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

A) 0.682
B) 0.232
C) 0.768
D) 0.303

Question 26

Two groups of people were asked their preference in television programs from among three new programs. The results are shown in the table below. What is the probability that a person selected at random will be from group A or prefer program X?

Question 27

The graduates at a southern university are shown in the table.

A student is selected at random from the graduating class.

-Find the probability that the student is male, P(M).

A) P(M) =
B) P(M) =
C) P(M) =
D) P(M) =

Question 28

The graduates at a southern university are shown in the table.

A student is selected at random from the graduating class.

-Find the probability that the student is female, given that the student is receiving an education degree, P(F|E).

A) P(F|E) =
B) P(F|E) =
C) P(F|E) =
D) P(F|E) =

Question 29

The graduates at a southern university are shown in the table.

A student is selected at random from the graduating class.

-Find the probability that the student is female, given that an education degree is not received, P(F|E').

A) P(F|E') =
B) P(F|E') =
C) P(F|E') =
D) P(F|E') =

Question 30

Use the tree diagram to find the requested probability:

-Find P(X $\mid$ A). Give your answer as a decimal and round your answer to three decimal places if necessary. a = 0.9, b = 0.1, c = 0.6, d = 0.4, e = 0.2, f = 0.8

A) 0.964
B) 0.54
C) 0.6
D) 0.675

Question 31

People were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. P(person is over 40 $\cap$ person drinks diet cola)?

A)
B)
C)
D)

Question 32

The table shows the political affiliation of voters in a small midwestern town and their positions on stronger drug control laws.

A) 0.350
B) 0.390
C) 0.420
D) 0.490

Question 33

A box contains 7 red balls and 3 white balls. Two balls are to be drawn in succession without replacement. What is the probability that the sample will contain exactly one white ball and one red ball?Determine independence.

Question 34

The table shows the political affiliation of voters in one city and their positions on stronger gun control laws.

Are party affiliation and position on gun control laws independent?

Question 35

The table lists the eight possible blood types. Also given is the percent of the U.S. population having that type. Let E be the event that a randomly selected person in the U. S. has type B blood. Let F be the event that a randomly selected person in the U. S. has RH-positive blood.Find P(F|E).

A) 0.340
B) 0.818
C) 0.720
D) 0.107

Question 36

The table lists the eight possible blood types. Also given is the percent of the U.S. population having that type. Let E be the event that a randomly selected person in the U. S. has type B blood. Let F be the event that a randomly selected person in the U. S. has RH-positive blood.Find P(E|F).

A) 0.107
B) 0.840
C) 0.182
D) 0.818

Question 37

People were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. Find P(person is over 40|person drinks root beer).

A)
B)
C)
D)

Question 38

Refer to the table below for events in a sample space, S, compute P(C|E).

Question 39

A class of 40 students has 10 honor students and 13 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.

Question 40

Each person in a group of students was identified by his or her hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are shown in the table below. Find the probability that a student preferred morning classes given that he or she has blonde hair.

Question 41

If 80% of scheduled flights actually take place and cancellations are independent events, what is the probability that 3 separate flights will all take place?

A) . 51
B) . 64
C) . 80
D) .0 1

Question 42

A calculator requires a keystroke assembly and a logic circuit. Assume that 98% of the keystroke assemblies and 93% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory. Assume that defects in keystroke assemblies are independent of defects in logic circuits.

A) . 8649
B) . 9600
C) . 9114
D) . 9604

Question 43

Use the tree diagram to find the requested probability:

-Find P(X $\mid$ A). Give your answer as a decimal and round your answer to three decimal places if necessary. a = 0.9, b = 0.1, c = 0.8, d = 0.2, e = 0.6, f = 0.4

A) 0.923
B) 0.514
C) 0.8
D) 0.72

Question 44

Use the tree diagram to find the requested probability:

-Find P(M $\mid$ Q). Give your answer as a fraction. a = 0.8, b = 0.2, c = 0.6, d = 0.2, e = 0.2, f = 0.5, g = 0.4, h = 0.1

A)
B)
C)
D)

Question 45

Find the probability:
-One urn has 4 red balls and 1 white ball; a second urn has 2 red balls and 3 white balls. A single card is randomly selected from a standard deck. If the card is less than 5 (aces count as 1), a ball is drawn out of the first urn; otherwise a ball is drawn out of the second urn. If the drawn ball is red, what is the probability that it came out of the second urn?Use Bayes' rule to find the indicated probability.

Question 46

Use Bayes' rule to find the indicated probability:

-In Cumberland County, 55% of registered voters are Democrats, 30% are Republicans and 15% are independent. During a recent election, 35% of the Democrats voted, 65% of the Republicans voted, and 75% of the independent voted. What is the probability that someone who voted is a Democrat?

A) 0.55
B) 0.615
C) 0.45
D) 0.385

Question 47

Use Bayes' rule to find the indicated probability:

-In Cumberland County, 55% of registered voters are Democrats, 30% are Republicans and 15% are independent. During a recent election, 35% of the Democrats voted, 65% of the Republicans voted, and 75% of the independent voted. What is the probability that someone who voted is a Republican?

A) 0.225
B) 0.39
C) 0.065
D) 0.385

Question 48

Use Bayes' rule to find the indicated probability:

-An water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R) = 0.53. The clay probability is P(C) = 0.21. The sand probability is P(S) = 0.26. It if it rock, a geological test gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test gives a 75% accuracy for sand. Given the test is positive, what is the probability that soil is rock, P(rock | positive)?

A) P(rock | positive) = 0.385
B) P(rock | positive) = 0.405
C) P(rock | positive) = 0.53
D) P(rock | positive) = 0.209

Question 49

Use Bayes' rule to find the indicated probability:

-An water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R) = 0.53. The clay probability is P(C) = 0.21. The sand probability is P(S) = 0.26. It if it rock, a geological test gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test gives a 75% accuracy for sand. Given the test is positive, what is the probability that soil is clay, P(clay | positive)?

A) P(clay | positive) = 0.53
B) P(clay | positive) = 0.385
C) P(clay | positive) = 0.209
D) P(clay | positive) = 0.405

Question 50

Use Bayes' rule to find the indicated probability:

-An water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R) = 0.53. The clay probability is P(C) = 0.21. The sand probability is P(S) = 0.26. It if it rock, a geological test gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test gives a 75% accuracy for sand. Given the test is positive, what is the probability that soil is rock, P(sand | positive)?

A) P(sand | positive) = 0.385
B) P(sand | positive) = 0.26
C) P(sand | positive) = 0.209
D) P(sand | positive) = 0.405

Question 51

Find the probability:
-A basketball team is to play two games in a tournament. The probability of winning the first game is .10. If the first game is won, the probability of winning the second game is .15. If the first game is lost, the probability of winning the second game is .25. What is the probability the first game was won if the second game is lost?Find the expected value.

Question 52

A car agency has found daily demand to be as shown in the table. Find the expected number of customers.

A) 12
B) 9
C) 2
D) 10

Question 53

Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability:

-Two marbles are drawn from a bag in which there are 4 red marble and 2 blue marble. The number of blue marbles is counted.

A)
B)
C)
D)

Question 54

Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability:

-Three coins are tossed, and the number of heads is noted.

A)
B)
C)
D)

Question 55

The number of loaves of whole wheat bread left on the shelf of a local quick stop at closing (denoted by the random variable X) varies from day to day. Past records show that the probability distribution of X is as shown in the following table. Find the probability that there will be at least three loaves left over at the end of any given day.

A) 0.65
B) 0.35
C) 0.15
D) 0.20

Question 56

The probability distribution for the random variable X is: What is the expected value of X?

A) 0.26
B) 0.62
C) 0.22
D) 0.50

Question 57

The payoff table for three possible courses of action , , and is given below.

Which course of action will produce the largest expected value? What is it?

Question 58

Mr. Cameron is sponsoring an summer concert. He estimates that he will make $300,000 if it does not rain and make $60,000 if it does rain. The weather bureau predicts the chance of rain is 0.34 for the day of the concert. What are Mr. Cameron's expected concert earning?

A) $60,000
B) $300,000
C) $360,000
D) $218,400

Question 59

Mr. Cameron is sponsoring an summer concert. He estimates that he will make $300,000 if it does not rain and make $60,000 if it does rain. The weather bureau predicts the chance of rain is 0.34 for the day of the concert. An insurance company is willing to insure the concert for $150,000 against rain for a premium of $30,000. If he buys this policy, what are his expected earnings from the concert?

A) $239,400
B) $300,000
C) $270,000
D) $180,000