a. A lumber company has just taken delivery on a

Chapter 2, Problem 86

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a. A lumber company has just taken delivery on a shipmentof 10,000 2 3 4 boards. Suppose that 20% ofthese boards (2000) are actually too green to be used infirst-quality construction. Two boards are selected atrandom, one after the other. Let A = {the first board is green} and B = {the second board is green}. ComputeP(A), P(B), and P(A B) (a tree diagram mighthelp). Are A and B independent?b. With A and B independent and P(A) = P(B) = .2,what is P(A B)? How much difference is therebetween this answer and P(A B) in part (a)? Forpurposes of calculating P(A B), can we assumethat A and B of part (a) are independent to obtainessentially the correct probability?c. Suppose the shipment consists of ten boards, of whichtwo are green. Does the assumption of independence now yield approximately the correct answer forP(A B)? What is the critical difference between thesituation here and that of part (a)? When do you thinkan independence assumption would be valid in obtainingan approximately correct answer to P(A B)?