A lumber company has ust taken delivery on a shipment of 10,000 2 X 4 boards. Su

Question

A lumber company has ust taken delivery on a shipment of 10,000 2 X 4 boards. Suppose that 0% of these boards 4000 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 P(A), P(B), and PIA n B) (a tree diagram might help). (Round your answer for A n B) to five decimal places.) P(B) PA n B)- Are A and B independent? o Yes, the two events are independent O No, the two events are not independent (b) with A and B independent and A)-A(B)-0.4, what is P(A n B)? How much difference is there between this answer and PCA ) in part (a)? o There is no difference. There is very little difference O There is a very large difference For purposes of calculating PA n B), can we assume that A and B of part (a) are independent to obtain essentially the correct probability? O Yes O No (c)Suppose the lat consists of ten boards, of which four are green. Does the assumption of independence now yield approximately the correct answer for P(A n B)? O Yes O No what is the critical difference between the situation here and that of part (a)? O The critical difference is that the percentage of green boards is smaller in part (a). O The cribical difference is that the percentage of green boards is larger in part (a) o The critical difference is that the population size in part (a) is small compared to the random sample of two boards O The eritical difference is that the population size in part (a) is huge 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)? o This assumption would be valid when the sample size is very large o This assumption would be valid when the papulation is much larger than the sample size. O This assumption would be valid when there are more green boards in the sample. o This assumption would be valid when there are fewer green boards in the sample.

Explanation / Answer

a) P(A) =4000/10000=0.4

P(B)=P( first board is green and second board is green +first board not green *second board green)

=(4000/10000)*(3999/9999)+(6000/10000)*(4000/9999)=0.40

P(AnB)=P( first board is green and second board is green) ==(4000/10000)*(3999/9999)=0.15998

as P(A)*P(B) is not equal to P(AnB)

No the to events are not independent

b) P(AnB)=P(A)*P(B)=0.16

there is avery little difference.

for purpose of .........correct probability------- Yes

c)

No

the critical difference is..........in part (a) is huge comared to the random sample...........

the assumption would be valid when the sample size is very large,

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