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MTH201: Probability and Statistics Quiz 1 Answers Date: February 4, 2015 1. A laboratory blood test is 99% e_ective in detecting a certain disease when it is, in fact, present. However, the test also yields a false positive result for 1% of the healthy persons tested. (That is, if a healthy person is tested, then, with probability 0.01, the test result will imply he or she has the disease.) If 0.5% of the population actually has the disease, what is the probability a person has the disease given that his test result is positive? Ans: 0.3322 2. Obtain the sample space of an experiment that consists of a fair coin being tossed four times. Consider the following events: a. A is the event all four results are the same. b. B is the event exactly one Head occurs. c. C is the event at least two Heads occur. Calculate P(A) + P(B) + P(C) Ans: 17/16 3. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with it. Now suppose that we draw another ball. Compute the probability that the first ball drawn was black given that the second ball drawn was red. 𝑏 Ans: 𝑏+𝑟+𝑐 4. Five people are sitting at a table in a restaurant. Two of them order coffee and the other three order tea. The waiter forgot who ordered what and puts the drinks in a random order for the five persons. Compute the size of the sample space and determine the probability that each person gets the correct drink. Ans: 0.1 5. There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. In how many ways can this be done? Ans: 21 6. Suppose that each of three men at a party throws his hat into the center of the room. The hats are first mixed up and then each man randomly selects a hat. What is the probability that none of the three men selects his own hat? 1 Ans: 3 7. An airport bus deposits 25 passengers at 7 stops. Each passenger is as likely to get o_ at any stop as at any other, and the passengers act independently of one another. The bus makes a stop only if someone wants to get off. What is the probability that somebody gets off at each stop? Ans: 0.8562 1