Given that events A and B are independent with P(A)=0.24P(A)=0.24 and P(B|A)=0.85P(B∣A)=0.85, determine the value of P(B)P(B), rounding to the nearest thousandth, if necessary.<…

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asked Jun 26, 2021 3.3k views

1 Answer

Chandrika Prajapati · Answer 1 · 2021-07-02T11:30:45+0000

Answer:

P(B) = 0.85

Explanation:

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

P(A) = 0.24, P(B|A) = 0.85

These events are independent.

This means that
$P(A \cap B) = P(A)*P(B)$ . So

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

P(B|A) = (P(A)*P(B))/(P(A))

P(B|A) = P(B)

So

P(B) = 0.85