Question

Given P(A)=0.63P(A)=0.63, P(B)=0.4P(B)=0.4 and P(A\text{ and }B)=0.332P(A and B)=0.332, find the value of P(B|A)P(B∣A), rounding to the nearest thousandth, if necessary.

Answer 1

Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Then to find the requested conditional probability we will substitute in the following formula:

$\begin{gathered} P(B|A)=\frac{P(A\cap B)}{P(A)} \\ =\frac{0.332}{0.63} \\ \approx0.53 \end{gathered}$

Finally we obtain that P(B|A) is approximately equal to 0.53.