Question

Evaluate P(A ∪ B), if 2P(A) = P(B) = \(\frac{5}{13}\) and P(A/B) = \(\frac{2}{5}\)

Answer 1

We have:

2P(A) = P(B) = \(\frac{5}{13}\)

⇒ P(A) = \(\frac{5}{26}\), P(B) = \(\frac{5}{13}\).

So, P(A/B) = \(\frac{P(A∩B)}{P(B)}\)

or \(\frac{2}{5}\) = \(\frac{P(A \cap B)}{\frac{5}{13}}\)

⇒ P(A ∩ B) = \(\frac{2}{5}\) × \(\frac{5}{13}\) = \(\frac{2}{13}\).

∴ P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= \(\frac{5}{26}\) + \(\frac{5}{13}\) – \(\frac{2}{13}\) = \(\frac{5+10-4}{26}\) = \(\frac{11}{26}\)