Question

A bag contains 3 white and 6 black balls while another bag containg 6 white and 3 black balls. A bag is selected at random and a ball is drawn. Find the probability that the ball drawn is of white colour.

Answer 1

E₁ = Event that bag I is selected

E₂ = Event that bag II is selected

E = Event that the ball drawn is of white colour.

So, P = (E₁) = 1/2,

P = (E₂) = 1/2

Also, P (E/E₁) = P (ball drawn is white when bag I is selected) = 3/9

P (E/E₂) = P (ball drawn is white when bag II is selected) = 6/9

By total propability theorem

Required propability = P (E) · P (E₁) + P (E₂) · P (E/E₂)