A bag contains 1 white and 6 red balls, and a second bag contains 4 white and 3 red balls. One of the bags is picked up at random and a ball is randomly drawn from it, and is found to be white in colour. Find the probability that the drawn ball was from the first bag.

Question

Philoid · Accepted Answer

Given:

Bag I has 1 white and 6 red balls

Bag II has 4 white and 3 red balls

Let us assume U₁, U₂ and A be the events as follows:

U₁ = choosing Bag I

U₂ = choosing Bag II

A = choosing white ball from urn

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 ball from each Bag differs from Bag to Bag and the probabilities are as follows:

⇒ P(A|U₁) = P(Choosing white ball from Bag I)

⇒

⇒ P(A|U₂) = P(Choosing white ball from Bag II)

⇒

Now we find

P(U₁|A) = P(The chosen ball is from Bag I)

Using Baye’s theorem:

⇒

∴ The required probabilities are .