Question

Let A and B be the events such that

2P(A) = P(B) = 5/13 and P(A/B) = 2/5.

Find

(i) P(A ∩ B)

(ii) P(A ∪ B).

Answer 1

Given - A and B be the events such that 2P(A) = P(B) = \(\frac{5}{13}\) and

P(A/B) = \(\frac{2}{5}\)

To find – 

(i) P(A ∩ B)

(ii) P(A ∪ B)

Formula to be used – By conditional probability, P(A/B) = \(\frac{P(A \cap B)}{P(B)}\) where P(A/B) is the probability of occurrence of the event 

A given that B has already occurred.