A lot of 1000 components contains 150 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. $\text { Find } P ( B \text { and } A ) \text {. }$
A) 0.0224
B) 0.1491
C) 0.15
D) 0.0067

Question

Quizplus · Accepted Answer

First, we can find the probability of drawing a defective component on the first draw, which is simply P(A) = 150/1000 = 0.15.

Since the first component drawn is defective, there are now only 999 components left, and 149 of them are defective. Thus, the probability of drawing a defective component on the second draw given that the first component was defective is P(B|A) = 149/999.

To find the probability of both A and B occurring, we use the formula for the probability of the intersection of two events:

P(A and B) = P(A) * P(B|A)

Plugging in our values, we get:

P(A and B) = (150/1000) * (149/999)

Simplifying, we get:

P(A and B) = 0.0224

So the answer is choice A.

A Lot of 1000 Components Contains 150 That Are Defective Find P(B and A). \text { Find } P ( B \text { and } A ) \text {. } Find P(B and A).

A Lot of 1000 Components Contains 150 That Are Defective $\text { Find } P ( B \text { and } A ) \text {. }$