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Homework 2 - University of California Los Angeles...

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University of California, Los Angeles Department of Statistics Statistics 100A Instructor: Nicolas Christou Homework 2 EXERCISE 1 The Statistics Society at a large university would like to determine whether there is a relationship between a student’s interest in statistics and his or her ability in mathematics. A random sample of 200 students is selected and they are asked whether their ability in mathematics and interest in statistics is low, average, or high. The results were as follows. Ability in Mathematics Low Average High Total Low 60 15 15 90 Interest in Statistics Average 15 45 10 70 High 5 10 25 40 Total 80 70 50 200 A person is randomly selected. a. What is the probability that the person has high interest in statistics? b. What is the probability that the person has high ability in mathematics and high interest in statistics? c. Given that the person has high ability in mathematics, what is the probability that the person has high interest in statistics? d. Are the events “high ability in mathematics” and “high interest in statistics” independent? EXERCISE 2 Suppose a woman tries on a dress. The probability that she asks for alterations is 0.65. The probability that she asks for delivery is 0.32. The probability that she asks for alterations and delivery is 0.21. Suppose that you randomly select a woman who has tried on a dress. What is the probability that:
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