A lot of 1000 components contains 350 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. a. Find P(A).b. Find P(B|A) .c. Find P(A ∩ B).d. Find P(Ac ∩ B).e. Find P(B) .f. Find P(A|B).g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.

Step-by-step explanation:

a.

Remember that in general, the probability of an event is

(number of cases)/ (total number of cases)

Therefore for this part it is 350/1000 = 0.35

b.

If A occurs then that means that a 349 elements are defective out of 999, therefore

349/999 = 0.34

c.

Remember that

(349/999)*(35/1000) = 0.01

d.

You are computing the probability that your first component is not defective and the second is, the probability that the first is not defective is 650/1000 and the probability that the second is defective is 350/999 therefore for the answer is

(650/1000)*(450/999) = 0.29

e.

Remember that

f.

For this part your can use Bayes theorem

= 0.39

g.

They are not at all. If one of them is defective that will definitely affect the probability of the other event.

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step-by-step explanation:

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