Question

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.

Answer 1

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)