A lumber company has just taken delivery on a shipment of 10,000 2 × 4 boards. S

Question

A lumber company has just taken delivery on a shipment of 10,000 2 × 4 boards. Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other. Let A-{the first board is green) and B = {the second board is green) (a) Compute PtA), P(8), and P(An ) (a tree diagram might help). (Round your answer for P(A n ) to five decimal places.) P(A n B) = Are A and B independent? Yes, the two events are independent. No, the two events are not independent. (b) With A and B independent and PA)-P B)0.1, what is PAn B)? How much difference is there between this answer and PA) in part (a)? There is no difference. There is very little difference. O There is a very large difference. For purposes of calculating PTA n ), can we assume that A and 8 of part (a)are independent to obtain essentially the corect probability? Yes No (c) Suppose the lot consists of ten boards, of which one are green. Does the assumption of independence now yield approximately the correct answer for Pa n 8)? Yes No What is the critical difference between the situation here and that of part (a)? The critical difference is that the population size in part (a) is huge compared to the andom sample of two boards. The critical difference is that the percentage of green boards is smaller in part (a). The critical difference is that the percentage of green boards is larger in part (a). The critical difference is that the population size in part (a) is small compared to the randon sample of two boards When do you think that an independence assumption would be valid in obtaining an approximately correct answer to PAnB)? This assumption would be valid when the sample size is very large. This assumption would be valid when there are fewer green boards in the sample. This assumption would be valid when the population is much larger than the sample size. Thls assumption would be valld when there are more green boards in the sample

Explanation / Answer

a) P(A) =0.1

P(B) =0.1

P(AnB) =P(first is green and second is green) =(1000/10000)*(999/9999)=0.00999

No the two events are not independent.

b)

P(AnB)= P(A)*P(B) =0.01

there is very little difference

YEs

c)

No

critical difference population size is huge

assumption is valid when the sample size is very large

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