A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

Given: let E_{1} be the event of choosing the bag I, E_{2} be the event of choosing the another bag say bag II and A be the event of drawing a red ball.

Then P (E_{1}) = P (E_{2}) = 1/2

Also P(A|E_{1}) = P (drawing a red ball from bag I)

And P(A|E_{2}) = 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(E_{1}|A).

By using bayes’ theorem, we have:

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