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

Question

asked Dec 13, 2021 39.0k views

1 Answer

Winster · Answer 1 · 2021-12-19T17:08:30+0000

Answer:

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

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