Question

There are two known issues with a certain model of new car. The first issue, A, occurs with a probability of P(A)=0.1. B is another known issue with the car. If it is known that either event occurs with a probability of P(A OR B)=0.93, and that both events occur with a probability of P(A AND B)=0.07, calculate P(B).

Answer 1

`P(B) = 0.90`

Explanation:

Given

`P(A) = 0.1`

`P(A\ or\ B) = 0.93`

`P(A\ and\ B) = 0.07`

Required

`P(B)`

To do this, we make use of:

`P(A\ or\ B) + P(A\ and\ B) = P(A) + P(B)`

Make P(B) the subject

`P(B) = P(A\ or\ B) + P(A\ and\ B) - P(A)`

So, we have:

`P(B) = 0.93 + 0.07 - 0.1`

`P(B) = 0.90`