Question

Given P(A)=0.78P(A)=0.78, P(B)=0.65P(B)=0.65 and P(A\cup B)=0.873P(A∪B)=0.873, find the value of P(A\cap B)P(A∩B), rounding to the nearest thousandth, if necessary

Answer 1

`P(A\ n\ B) = 0.557`

Explanation:

Given

`P(A) = 0.78`

`P(B) = 0.65`

`P(A\ u\ B) = 0.873`

Required

Determine
`P(A\ n\ B)`

From laws of probability, we have:

`P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)`

Substitute in values

`P(A\ n\ B) = 0.78 + 0.65 - 0.873`

`P(A\ n\ B) = 0.557`

Hence,
`P(A\ n\ B)` is calculated to be 0.557