Question

A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A) = .6 and P(B) = .5. What is P(B|A)?

Answer 1

Answer:
`P(B|A)=(5)/(6)`

Explanation:

Given Events :

A = Next component brought in for repair is an audio component.

B= Next component is a compact disc player.

Also, P(A)=0.6 and P(B)=0.5

Since B is contained in A.

So, A∩B = B

Then, P(A∩B)=P(B) = 0.5

Conditional probability formula :

`P(B|A)=(P(A\cap B))/(P(A))`

Substitute values , we get

`P(B|A)=(0.5)/(0.6)=(5)/(6)`

Hence,
`P(B|A)=(5)/(6)`