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

Answer:

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

Step-by-step 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