# Chapter 1. Independence and Multiplication Rule

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1:13

### Question 1.1

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Correct. These events are not disjoint. Logic tells us that there are houses with both a swimming pool and a garage.
Incorrect. These events are not disjoint. Logic tells us that there are houses with both a swimming pool and a garage.
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3:38

### Question 1.2

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Correct. These events are dependent. Homes with swimming pools tend to be “premium” homes. Premium homes are more likely to have garages.
Incorrect. These events are dependent. Homes with swimming pools tend to be “premium” homes. Premium homes are more likely to have garages.
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### Question 1.3

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Correct. While each student has his or her own strengths and weaknesses, strong students will tend to do well in both classes and weaker students will tend to do poorly in both, so these events are dependent.
Incorrect. While each student has his or her own strengths and weaknesses, strong students will tend to do well in both classes and weaker students will tend to do poorly in both, so these events are dependent.
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### Question 1.4

Correct. Because conditions are likely to be different on the two days, knowing Monday’s flight was on time (or not), won’t change the probability that Wednesday’s flight will be on time.
Incorrect. Because conditions are likely to be different on the two days, knowing Monday’s flight was on time (or not), won’t change the probability that Wednesday’s flight will be on time.
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3:55

### Question 1.5

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Correct. If you are drawing one Skittles from the bag it cannot be two different colors; these are disjoint events, so they are not independent.
Incorrect. If you are drawing one Skittles from the bag it cannot be two different colors; these are disjoint events, so they are not independent.
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5:59

### Question 1.6

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Correct. Because we are selecting at random from a large population, the randomly selected students are independent. P(Comm and Business) = P(Comm)P(Business) = 0.2(0.15) = 0.03.
Incorrect. Because we are selecting at random from a large population, the randomly selected students are independent. P(Comm and Business) = P(Comm)P(Business) = 0.2(0.15) = 0.03.
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7:29

### Question 1.7

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Correct. The first toss won’t affect the result of the second, so the tosses are independent. The probability both tosses land heads up is 0.55*0.55.
Incorrect. The first toss won’t affect the result of the second, so the tosses are independent. The probability both tosses land heads up is 0.55*0.55.
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### Question 1.8

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Correct. In Chapter 10, you learned that “at least one” means “not 0,” so the probability of at least one head is 1 – P(all tails). Each toss is a tail with probability 1 – 0.55 = 0.45, so the desired probability is 1 – 0.455. Notice that we have used the “event A does not occur” rule twice in this exercise as well as the general multiplication rule.
Incorrect. In Chapter 10, you learned that “at least one” means “not 0,” so the probability of at least one head is 1 – P(all tails). Each toss is a tail with probability 1 – 0.55 = 0.45, so the desired probability is 1 – 0.455. Notice that we have used the “event A does not occur” rule twice in this exercise as well as the general multiplication rule.
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9:08

### Question 1.9

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Correct. While most English majors dislike math enough not to major in it as well, it is not impossible for a student to do both. These events are neither disjoint nor independent.
Incorrect. While most English majors dislike math enough not to major in it as well, it is not impossible for a student to do both. These events are neither disjoint nor independent.
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