A bag A contains 2 white and 3 red balls and a bag B contains 4 white and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from bag B.

Question

Philoid · Accepted Answer

Given:

Bag A has 2 white and 3 red balls

Bag B has 4 white and 5 red balls

Let us assume B₁, B₂, B₃ and A be the events as follows:

B₁ = choosing Bag I

B₂ = choosing Bag II

A = choosing red ball from Bag

We know that each Bag is most likely to choose. So, probability of choosing a bag will be same for every bag.

⇒

The Probability of choosing balls from each Bag differs from bag to bag and the probabilities are as follows:

⇒ P(A|B₁) = P(Choosing red ball from Bag 1)

⇒

⇒ P(A|B₂) = P(Choosing red ball from Bag 2)

⇒

Now we find

P(B₂|A) = P(The chosen ball is from bag2)

Using Baye’s theorem:

⇒

∴ The required probabilities are .