3) In a certain community, 36 percent of the families own a dog and 22 percent o

Question

3) In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is (a) The probability that a randomly selected family owns both a dog and a cat? (b) The conditional probability that a randomly selected family owns a dog given that it owns a cat? 4) Fifty-two percent of the students at a certain college are females. Five percent of the students in this college are majoring in computer science. Two percent of the students are women majoring in computer science. If a student is selected at random, find the conditional probability that (a) The student is female given that the student is majoring in computer science; (b) This student is majoring in computer science given that the student is female 5) There are 15 tennis balls in a box, of which 9 have not previously been used Three of the balls are randomly chosen, played with, and then returned to the box Later, another 3 balls are randomly chosen from the box. Find the probability that None of these balls has ever been used 6) A family has j children with probability pj, where p1 = 0.1 , p2 = 0.25, p3 = 0.35. p4 = 0.3. A child from this family is randomly chosen. Given that this child is the eldest child in the family, find the conditional probability that the family has a) Only 1 child; b) 4 children 7) Three cooks, A, B, and C, bake a special kind of cake, and with respective probabilities 0.02, 0.03, and 0.05, it fails to rise. In the restaurant where they work, A bakes 50 percent of these cakes, B 30 percent, and C 20 percent. What proportion of "failures" is caused by A?

Explanation / Answer

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3.

a. P( family owns both dog and cat) = .22 ( given in the question)

b. P( family owns dog given it owns a cat) = P( family owns both given it owns cat)

=Probability that it owns both / Probability it owns cat

= .22/.30

= .7333

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