Problem sets chap 5 Part III 4.70 Find the joint probability of A and B for the

Question

Problem sets chap 5 Part III 4.70 Find the joint probability of A and B for the following. a) P(A) = .40 and P(B/A) = .25 P(B) = .65 and P(A/B) = .36 b) 4.71 Find the joint probability of A and B for the following. a) P(B).59 and P(A/B) 77 b) P(A)-,28 and PCB/A)-35 4.72 Given that A and B are two independent events, find their joint probability for the following. a. P(A) = .61 and P(B) = .27 b, P(A) = .39 and P(B) = .63 4.73 Given that A and B are two independent events, find their joint probability for the following. a. P(A) = .20 and P(B) .76 b. P(A) .57 and P(B) .32 4.74 Given that A, B, and C are three independent events, find their joint probability for the following. a. P(A)-20, P(B) = .46, and P(C) = .25 b, P(A) = .44, P(B) = .27, and P(C) = .43 4.81 The following table gives a two-way classification of all basketball players at a state university who began their college careers between 1988 and 1998, based on gender and whether or not they graduated. Did Not Graduate Male Female Graduated 126 133 32 a. If one of these players is selected at random, find the following probabilities i. P(female and graduated) i. P(male and did not graduate) b. Find P(graduated and did not graduate). Is this probability zero? If yes, hy?

Explanation / Answer

P(A)=0.4 and P(B|A)=0.24 thus the joint probability is given by P(A and B)=P(B|A)*P(A)=0.4*0.25 =0.1

P(B)=0.65 and P(A|B)=0.36 thus probability P(A and B)=P(B)*P(A|B)=0.65*0.36=0.234

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