Question

The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?A. 0.05B. 0.15C. 0.45D. 0.50E. 0.55

Answer 1

C.
`P(B) =0.45`

Explanation:

We have been given that the probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. The probability that either event A or event B occurs is 0.6. We are asked to find the probability that event B will occur.

We have been given
`P(A) = 0.4`,
`P(A\cap B) = 0.25` and
`P(A\cup B) = 0.6`.

We will use the formula
`P(A)+P(B) =P(A\cup B)+P(A\cap B)`.

Upon substituting our given values in above formula, we will get:

`0.4+P(B) =0.60+0.25`

`0.4+P(B) =0.85`

`0.4-0.4+P(B) =0.85-0.4`

`P(B) =0.45`

Therefore, the probability that event B will occur is 0.45 and option C is the correct choice.