There are two bags, Bag I and Bag II. Bag I contain 4 white and 3 red balls while another Bag II contains 3 white and 7 red balls. One ball is drawn at random from one of the bags and it is found to be white. Find the probability that it was drawn from Bag I.

OR

If , find the value of x.

We are given that,

Bag I: 4 white and 3 red balls

Bag II: 3 white and 7 red balls

The ball drawn at random is white ball.

We need to find the probability of the white ball being drawn from Bag I.

Since, the ball is drawn at random, the probability of drawing a ball from Bag I is 1/2 and the probability of drawing a ball from Bag II is 1/2.

From Bag I:

Probability of drawing white ball from Bag I

⇒Probability ofdrawing white ball from Bag I amongst both bags

From Bag II:

Probability of drawing white ball from Bag II

⇒Probability of drawing white ball from Bag II amongst both bags

Probability of drawing white ball from Bag I is given by,

Thus, probability that the white ball was drawn from Bag I is 40/61.