1 Answer

Drobertson · Answer 1 · 2020-10-14T03:08:46+0000

Answer:

$P(A\textrm{ and }B)=(3)/(14)$

Explanation:

Given:

P(A)=(4)/(7)

P(B|A)=(3)/(8)

We know that, conditional probability of B given that A has occurred is given as:

$P(B|A)=(P(A\cap B)/(P(A))$ . Expressing this in terms of
$P(A\cap B)$ , we get

$P(A\cap B)=P(B|A)* P(A)$

Plug in the known values and solve for
$P(A\cap B)$ . This gives,

$P(A\cap B)=P(B|A)* P(A)\\P(A\cap B)=(3)/(8)* (4)/(7)\\P(A\cap B)=(12)/(56)=(3)/(14)$

Therefore, the probability of events A and B occurring is
.

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