Problem 24E

A lot of 1000 components contains 300 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.

Answer :

Step 1 of 8 :

Given, 300 are defective in a lot of 1000 components. Two components are drawn at random and tested.

Let A be the event that the first component drawn is defective and B be the event that the second component drawn is defective.