Chapter 1. Probability Rules

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Questions 1-2

1:29

Question 1.1

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Correct. These events are not disjoint. The Jack, Queen, and King of hearts are both face cards and hearts.

Incorrect. These events are not disjoint. The Jack, Queen, and King of hearts are both face cards and hearts.

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Question 1.2

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Correct. A = {GGG} for all girls. B = {BBB, BBG, BGB, GBB} for less than two girls. The outcome GGG is not in B, so the two events are disjoint.

Incorrect. A = {GGG} for all girls. B = {BBB, BBG, BGB, GBB} for less than two girls. The outcome GGG is not in B, so the two events are disjoint.

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Questions 3-5

2:21

Question 1.3

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Correct. Events P and C and I all occurring at the same time (in the same complex) would be P and C and I.

Incorrect. Events P and C and I all occurring at the same time (in the same complex) would be P and C and I.

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Question 1.4

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Correct. At least one of the amenities would be P or C or I. This includes the possibility of having all three.

Incorrect. At least one of the amenities would be P or C or I. This includes the possibility of having all three.

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Question 1.5

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Correct. The probabilities sum to 0.17 + 0.15 + 0.23 + 0.13 + 0.34 = 1.02. This is more than 1, so the distribution is not legitimate. Either someone in the registrar’s office has misclassified some students, or there are students with double majors that span the categories.

Incorrect. The probabilities sum to 0.17 + 0.15 + 0.23 + 0.13 + 0.34 = 1.02. This is more than 1, so the distribution is not legitimate. Either someone in the registrar’s office has misclassified some students, or there are students with double majors that span the categories.

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Questions 6-8

5:55

Question 1.6

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Correct. The probability of the entire sample space must be 1, and these options cover all possible majors. Subtract the total of the given probabilities from 1 to find P(Other).

Incorrect. The probability of the entire sample space must be 1, and these options cover all possible majors. Subtract the total of the given probabilities from 1 to find P(Other).

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Question 1.7

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Correct. Recycling at least some of the time means the student is not in the “Never” category. Also, these outcomes are disjoint (students could only select one answer). The desired probability is 1 – 0.05. Note that you could also add the probabilities of the three categories for people who do recycle.

Incorrect. Recycling at least some of the time means the student is not in the “Never” category. Also, these outcomes are disjoint (students could only select one answer). The desired probability is 1 – 0.05. Note that you could also add the probabilities of the three categories for people who do recycle.

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Question 1.8

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Correct: Recycling most of the time logically means the student is in the “Always” or “Usually” categories. Also, these outcomes are disjoint (students could only select one answer). The desired probability is 0.55 + 0.25.

Incorrect. Recycling most of the time logically means the student is in the “Always” or “Usually” categories. Also, these outcomes are disjoint (students could only select one answer). The desired probability is 0.55 + 0.25.

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