Understanding the solution of this probability problem

44 Views Asked by At

Given the following data:

P(B) = 0.02
P(B|A) = 0.94
P(A|B) = P(A'|B') = x

Now we solve the following equation to get the x

$ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A|B)P(B)}{P(A|B)P(B) + \boldsymbol{P(A|B')} P(B')} = \frac{0.02x}{0.02x + \boldsymbol{P(A|B')} 0.98}$

So I know that $\boldsymbol{P(A|B')}$ is supposed to be $(1-x)$ apparently, but how exactly is that derived?