a. A lumber company has just taken delivery on a lot of 10,000 2 x 4 boards. Suppose that 20% of these boards (2000) are actually too green to be used in rst-quality construction. Two boards are selected at random, one after the other. Let A = {the rst board is green} and B = {the sec- ond board is green}. Compute P(A), P(B), and P(A n B) (a tree diagram might help). Are A and B independent?
b. With A and B independent and P(A) = P(B) = .2, what is P(A n B)? How much difference is there between this answer and P(A n B) in part (a)? For purposes of calculating P(A n B), can we as- sume that A and B of part (a) are independent to obtain essentially the correct probability?
c. Suppose the lot consists of ten boards, of which two are green. Does the assumption of independence now yield approximately the cor- rect answer for P(A n B)? What is the critical difference between the situation here and that of part (a)? When do you think that an indepen- dence assumption would be valid in obtaining an approximately correct answer to P(A n B)?