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Question 48

There are two bags, one of which contains 3 black and 4 white balls, while the other contains 4 black and 3 white balls. A dice is cast. If the face 1 or 3 turns up, a ball is taken from the first bag and if any other face turns up a ball is chosen from the second bag. The probability of choosing a black ball is

Solution

Bag1 = 3 back, 4 white balls

Bag2 = 4 black, 3 white balls

Probability of selecting bag 1 = 2/6 = 1/3

Probability of selecting bag 2 = 1 - 1/3 = 2/3

Probability of choosing a black ball from bag 1 = 3/7

Probability of choosing a black ball from bag 2 = 4/7

Required probability = 1/3 * 3/7 + 2/3 * 4/7

= $$\frac{11}{21}$$

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