​ If P(B) = 3/5 and P(A’ ∩ B) = 1/2 for two events A and B, find P(A|B). ​

Question

If P(B) = \(\frac{3}{5} \)and P(A’ ∩ B) = \(\frac{1}{2}\) for two events A and B, find P(A|B).

Answer 1

P(B) = \(\frac{3}{5}\)and P(A’ ∩ B) = \(\frac{1}{2}\) are given.

∴ P(A’ ∩ B) = P(B) – P(A ∩ B)

∴ \(\frac{1}{2} = \frac{3}{5}\) – P(A ∩ B)

∴ P(A ∩ B) = \(\frac{3}{5} – \frac{1}{2} = \frac{6−5}{10 }= \frac{1}{10}\)

Now, P(A|B) = \(\frac{P(A∩B)}{P(B)}\)

= \(\frac{1}{10}\frac{3}{5} = \frac{1}{10}×\frac{5}{3} = \frac{1}{6}\)

∴ P(A|B) = \(\frac{1}{6}\)