can't finding B event under not A event in Bayes Theorem

Question

The conditional probability Pr[B|A] is 4/5; the conditional probability P[B|not A] is 2/5, and the unconditional probability of B is 1/2. What is the probability of A?

I know P(A) = (P(A/B) * P(B)) / P(B/A)

But I can't know how to get P(B/not A) from these probabilities.

Thanks in advance.

Answer 1

$$P(B)=P(A)P(B|A)+P(\overline {A})P(B|\overline {A})$$

$P(\overline {A})=1-P(A)$

... I think you are all set

Answer 2

HINT: Write the law of total probability for $P(B)$ conditioned on $A$.