A lumber company has Just taken delivery on a shipment of 10, 000 2 times 4 boar

Question

A lumber company has Just taken delivery on a shipment of 10, 000 2 times 4 boards. Suppose hat 40% of these boards (4000) are actual too green to be used n first quality construction. Two boards are selected at random, one after other. Let A = { the first board is green) and B = {the second board is green}. (a) Compute P(A), P(B), and p(A Intersection B) (a tree diagram might help) (Round your answer for P(A Intersection B) to five decimal places.) P(A) = P(B) = P(A Intersection 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 p(A) = P(B) = 0.4, what is P(A Intersection B)?

Explanation / Answer

A = {the first board is green}

B = {the second board is green}

We are given: P(A)=4000/10000= 0.4.

P(A') = 1 – P(A) = 1 – 0.4= 0.6

P(AB)=P(B|A)P(A)

where P(B|A) = 3999/9999=0.499

P(AB)=0.499*0.4=0.1996

P(B) =0.4

YES THE TWO EVENTS ARE INDEPENDENT

THEN P(AB)= 0.4*0.4=0.16

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