MATH 1680 Elementary Probability and Statistics HW 04 Name: 1. A travel agency surveyed 125 potential customers. The following information was obtained: 68 wished to travel to Hawaii, 53 wished to travel to Las Vegas, and 47 wished to travel to Orlando. Moreover, 34 wished to travel to Hawaii and Las Vegas, 26 wished to travel to Las Vegas and Orlando, 23 wished to travel to Hawaii and Orlando, and finally, 18 wished to travel to all three top destinations. Answer the following questions using the provided Venn diagram. (a) If you select a customer at random, what is the probability that the selected customer wanted to travel to none of the top three destinations mentioned? (b) If you select a customer at random, what is the probability that the selected customer wanted to travel to Orlando and Las Vegas, but not Hawaii? (c) If you select a customer at random, what is the probability that the selected customer wanted to travel to Orlando or Las Vegas, but not Hawaii? (d) If you select a customer at random, what is the probability that the selected customer wanted to travel to exactly two of the top three destinations mentioned in the problem? (e) If you select a customer at random, what is the probability that the selected customer wanted to travel to at least two of the top three destinations mentioned in the problem? 2 INSTRUCTOR: BYUNGIK KAHNG 2. According to an article, Tuberculin skin test, by J.B. Bass, in Tuberculosis in Workplace, M.J. Field, editor, (2001), National Academic Press, the reliability of Tuberclin Skin Test (TST) for apparently healthy U.S. population is as follows: If the subject has TB, the test comes back positive about 96% of the time (the sensitivity of the test is about 0.96), and if the subject does not have TB, the test comes back negative about 99.5% of the time (the specificity of the test is about 0.995). A recent report by Center for Disease and Control (http://www.cdc.gov/mmwr/preview/mmwrhtml/rr4906a1.htm) says, the children entering school in the U.S. have about 0.5% prevalence of the tuberculosis infection, on average. (a) What is the probability that the tested child has TB if the test result is positive? (b) What is the probability that the tested child has TB if the test result is negative