$P(B)$ given $P(A)$ = 0.12, $P(B | A)$ = 0.74 and $P(B | ¬A)$ = 0.2

Question

I have tried solving for $P(B)$ by expanding $P(B|A)$ but it just ends in

.12 * .74 = (.74 * .12) * $P(B)$/$P(B)$

I can't seem to find any way of solving for $P(B)$

Answer 1

You can use the law of total probability to write

$$P(B)=P(B|A)P(A)+P(B|A^c)P(A^c)$$ and plug in your values for $P(A)$, $P(B|A)$, $P(B|A^c)$. You can get $P(A^c)$ from $P(A^c)=1-P(A)$.