A bag contains 4

Given: let E₁ be the event of choosing the bag I, E₂ be the event of choosing the another bag say bag II and A be the event of drawing a red ball.

Then P (E₁) = P (E₂) = 1/2

Also P(A|E₁) = P (drawing a red ball from bag I)

And P(A|E₂) = P (drawing a red ball from bag II)

Now the probability of drawing a ball from bag I, being given that it is red, is P(E₁|A).

By using bayes’ theorem, we have: