Question

The bag ‘A’ contains 5 white and 3 black balls while the bag ‘B’ contains 4 white and 7 black balls. One of the bags is chosen at random and a ball is drawn from it. What is the probability that the ball is white?

Answer 1

Let E₁ be the event that bag A is chosen, 

E₂ be the event that bag B is chosen and A be the event that white ball is drawn. 

Note that E₁ and E₂ are mutually exclusive and exhaustive events. 

Since one of the bag is chosen at random, so

\(P(E_1) = \frac {1}{2},P(E_2 ) = \frac {1}{2}\)

P(A|E₁) = probability of drawing a white ball from bag

A = 5/8

P(A|E₂) = probability of drawing a white ball from bag

B = 4/11

By using law of total probability, we get 

P(A) = P(E₁) P(A|E₁) + P(E₂) P(A|E₂)