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Question -

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.



Answer -

Let E1 bethe event of choosing the bag I, E2 be the event of choosingthe 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) = 4/8 = ½

And P (A|E2)= P (drawing a red ball from bag II) = 2/8 = ¼

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

By using Bayes’theorem, we have:

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