A lumber company has ust taken delivery on a shipment of 10,000 2 A = {the first

Question

A lumber company has ust taken delivery on a shipment of 10,000 2 A = {the first board is green)and 8-(the second board is green} 4 boards. Suppose that 40% of these boards (4000) are actually too green to be used in first-quality construction. To boards are selected at random, one after the other. Let (a) Compute P(A), P(B), and a(A n 8) (a tree diagram might help). (Round your answer for pA n B} to five decimal places.) Are A and B independent? Yes, the two events are Independent. O No, the two events are not independent. (b) With A and B independent and PYA)P(B)0.4, what is PAn B)? How much differance is there hatween this answer and PA B) in part (a)? There is no difference. There is very little difference. O There is a very large difference. For purposes of calculating P(An B), can wa assume that A and of part (independent to obtain essentially the correct probability? Yes No (c) Suppose the lot consists of ten boards, of which four are green. Does the assumption of independence now yield approximately the correct answer for P(A· B)? O Yes No What is the critical difference between the situation here and that of part (a)? The critical difference is that the percentage of green boards is smaller in part (a) The critical difference is that the population size in part (a) is huge compared to the random sample of two boards. The critical difference is that the percentage of green baards is larger in part (a). The critical difference is that the population size in part (a) is small compared to the random sample of two boards. When do you think that an independence assumption would be valid in obtaining an approximately correct answer to PAn B)? This assumption would be valid when the sample size is very large. This assumption would be valid when the population is mch larger than the sample size. This assumption would be valid when there are more green boards in the sample This assumption would be valid when there are fewer green boards in the sample.

Explanation / Answer

a)P(A) =0.4

P(B) =0.4

P(A n B)=(4000/10000)*(3999/9999)=0.15998

No the two events are not independent

b)

P(A n B) =0.4*0.4 =0.16

there is a very little difference

Yes

c)

No

the critical difference is that the population size in part (a) is huge compared to the random sample of two boards

this assumption would be valid when the population size is much larger than the sample size

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