Question

A lot of 1115 components contains 275 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 dràwn is defective.

1) Find P(A).
2) Find P(BIA).
3) Find P(AnB)

Answer 1

1) P(A) = 0.2466

2) P(B|A) = 0.246

3) P(AnB) = 0.0607

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

1) Find P(A).

This is the probability that the first component is defective.

1115 components, of which 275 are defective. So

P(A) = 275/1115 = 0.2466

2) Find P(BIA).

This is the probability that the second component is defective, given that the first is.

Now there are 1114 components, of which 274 are defective. So

P(BIA) = 274/1114 = 0.246

P(B|A) = 0.246

3) Find P(AnB)

P(AnB) = P(A)*P(BIA) = 0.2466*0.246 = 0.0607

P(AnB) = 0.0607