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)=(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)=(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)