Question

Given that events A and B are independent with P(A)=0.15 and P(B)=0.36, determine the value of P(B∣A), rounding to the nearest thousandth, if necessary.

Answer 1

In order to calculate P(B|A), that is, the probability of B given A, we can use the following formula:

$P(B|A)=\frac{P(B\cap A)}{P(A)}$

Since the events are independent, we also have the following:

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

So we have that:

$\begin{gathered} P(B|A)=\frac{P(B)\cdot P(A)}{P(A)} \\ P(B|A)=P(B) \\ P(B|A)=0.36 \end{gathered}$

So the probability of B given A is 0.36.

(The probability of B given A being the same probability of B makes sense, since the events are independent, so A happening does not affect B)