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Q1. Assume that a couple has three children. a) And their youngest child is a girl. Calculate the probability that they have three girls. (Explain your answer!) b) If this couple has one boy, calculate the probability that the other two are girls. (Explain your answer!) Q2. In a certain neighborhood, 68 percent of the families own a house and 75 percent of the families that own a house also own a car. In addition, 90 percent of the families not owning a house own a car. a) Calculate the probability that a randomly selected family owns both a house and a car? a) The conditional probability that a randomly selected family owns a house given that it owns a car? Q3. Test results of three different courses from 100 samples are summarized as follows: Successful? Yes No Course 18 8 Course 2 36 5 Course 3 23 10 Let A denote the event that a sample is from course 1, and let B denote the event that a sample is successful. (a) Are events A and B independent? Why, Why not? (b) Determine (A|B) and (B|A). Q4. A box in a certain supply room contains 15 green balls and 8 red balls. Suppose that four balls are randomly selected without replacement. (a) What is the probability that exactly two of the selected balls are red? (b) What is the probability that at least one of the selected balls are green? (c) Suppose that there are now 15 green balls and 8 red balls and 4 yellow balls. What is the probability that exactly one of the selected balls are red and exactly one of the selected balls are yellow? (d) Suppose now that balls are to be selected one by one until a red ball is found. What is the probability that it is necessary to examine at least eight balls? (There are 15 green balls and 8 red balls) Q5. A real estate agent is showing homes to a prospective buyer. There are twelve homes in the desired price range listed in the area. The buyer has time to visit only five of them. a. In how many ways could the five homes be chosen if the order of visiting is considered? b. In how many ways could the five homes be chosen if the order is disregarded? c. If eight of the homes are new and four have previously been occupied and if the five homes to visit are randomly chosen, what is the probability that exactly four of the homes to visit are new