StatTutor Lesson - Independence and Multiplication Rule

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Independence and the multiplication rule
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      Question 1

      73

      Question 1.

      Are the events A = {randomly selected house has a swimming pool} and B = {randomly selected house has a garage} disjoint?

      A.
      B.

      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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      Questions 2-4

      218

      Question 2.

      Are the events A: a random house has a swimming pool and B: a random house has a garage independent or dependent?

      A.
      B.

      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 5

      235

      Question 5.

      Are the events A: drawing an orange Skittles from a bag and B: drawing a red Skittles from a bag independent or dependent?

      A.
      B.

      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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      Question 6

      359

      Question 6.

      At a large university, 15% of students are business majors and 20% are communications majors. If two students are selected at random, what is the probability the first is a communications major and the second is a business major?

      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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      Questions 7-8

      449

      Question 7.

      A bent coin has probability 0.55 of landing heads up. What is the probability that two tosses of the coin will both result in heads? Use four decimal places in your answer.

      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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      Questions 9-10

      548

      Question 9.

      To find the probability that a randomly chosen student has a double major in English and Mathematics, you would use

      A.
      B.
      C.

      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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