A shipment of 5000 printed circuit boards contains 42 that are defective. Two bo

Question

A shipment of 5000 printed circuit boards contains 42 that are defective. Two boards will be chosen at random, without replacement. Consider the two events E1 = event that the first board selected is defective and E2 = event that the second board selected is defective.

(a) Are E1 and E2 dependent events?

YesNo    

(b) Let not E1 be the event that the first board selected is not defective (the event E1c). What is P(not E1)?

(c) How do the two probabilities P(E2 | E1) and P(E2 | not E1) compare?

(d) Based on your answer to Part (c), would it be reasonable to view E1 and E2 as approximately independent?

YesNo   

Explanation / Answer

a) yes they are independent

b) probabiilty of defective is =42/5000=0.0084

probability not defective is 1-0.0084= 0.9916

c) P(E2 | E1) >>P(E2 | not E1)

d) no

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