Given that events A and B are independent with P(A)=0.85 and P(B) = 0.3,determine the value of P(A|B), rounding to the nearest thousandth, if necessary.

Question

asked Feb 21, 2023 149k views

1 Answer

Mr Grok · Answer 1 · 2023-02-28T02:25:49+0000

The Solution.

Given that

$\begin{gathered} P(A)=0.85 \\ P(B)=0.3 \end{gathered}$

The conditional probability P(A/B) is given as

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

But for independent events, we have that

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

Hence, it follows that

$\begin{gathered} P(A|B)=(P(A)* P(B))/(P(B))=P(A)=0.85\approx0.850 \\ \text{though the nearest thousandth is not necessary.} \end{gathered}$

Therefore, the correct answer is 0.85 ( 0.850 if you consider it necessary)