$A$ and $B$ are events with $P(A)=0.2, P(B)=0.6$ and $P(B|A)=0.9$.
Find $P(B|\bar{A})$, giving answers to within $1\%$ of the exact value.
The problem is shown in the image above. I need to find P(B given not A), however I am getting an answer of -0.3 which doesn't make sense.
I am applying the following equation:
$$P(B)=P(B|A)+P(B|\bar{A})$$
The Law of total probability is as follows, $$P(B)=P(B|A)P(A)+P(B|\bar{A})P(\bar{A})$$
some terms are missing from your equations. Hence, the error.