Bag I contains 3 red and 4 black balls and Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from Bag II.

Given, Two bags are given, in which 3 red and 4 black balls in I bag and 5 Red and 6 black balls in Bag II.

To Find: Find the probability that it was drawn from Bag II.

Explanation: Let us Consider some Assumption

E₁=Ball selected in Bag I

E₂=Ball selected in Bag II

A=selected Ball is Red

B=selected Ball is Black

Now, We need to find a red ball drawn from bag II.

That means, P(E₂|A)

Now,

P(E₁)=

P(E₂)=

(A|E₂)= Probability of red ball was selected from Bag II

P(A|E₂)=

P(A|E₂)=

(A|E₁)= Probability of red ball was selected from Bag I

P(A|E₁)=

P(A|E₁)=

Now,

Hence, The required probability is