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2 Exercises to be solved with detailed solutions Exercise 2.1 (8pts) An insurance company believes that people can be divided into two classes - those who are prone to have accidents and those who are not. The data indicate that an accident-prone person will have an accident in a 1-year period with probability 0.1. The probability for all others to have an accident in a 1-year period is 0.05. Suppose that the probability is 0.2 that a new policyholder is accident prone. What is the probability that a new policyholder will have an accident in the first year? Exercise 2.2 A total of 52% of voting-age residents of a certain city are Republicans, and the other 48% are Democrats. Of these residents, 64% of the Republicans and 42% of the Democrats are in favor of discontinuing affirmative action city hiring policies. A voting-age resident is randomly chosen. a. (5pts) What is the probability that the chosen person is in favor of discontinuing affirmative action city hiring policies? b. (10pts) If the person chosen is against discontinuing affirmative action hiring policies, what is the probability she or he is a Republican? Hint: Draw a probability tree diagram. Exercise 2.3 The defective rate of new computers is 5%. Let X be the number of defective computers in a batch of 100 computers. a. (3pts) What is the distribution of the random variable X? b. (2pts) Find the expected value E( X). c. (5pts) Find the probability that in this batch of 100 computers none are defective, d. (5pts) Find the probability that in this batch of 100 computers at least 4 are defective