Question

Out of two bags, bag I contains 3 red and 4 white balls and bag II contains 8 red and 6 white balls. A die is thrown. If it shows а number less than 3, then a ball is drawn at random from bag I, otherwise a ball is drawn at random from bag II. Find the probability that the ball drawn from one of the bags is a red ball.

Answer 1

Die shows number less than 3: {1, 2}

`P(B_1) = 2/6 = 1/3, P(B_2) = 4/6 = 2/3`

`P(R|B_1) = 3/7, P(R|B_2) = 8/14 = 4/7`

Required probability:

`P(R) = P(B_1)P(R|B_1) + P(B_2)P(R|B_2)`

= `1/3 * 3/7 + 2/3 * 4/7`

= `1/7 + 8/21`

= `(3 + 8)/21`

= `11/21`

Hence, the probability that the ball drawn from one of the bags is a red ball is `11/21`.