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NDA Math Probability

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Question : 92 of 100

Marks: +1, -0

There are 4 white and 3 black balls in a box In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black, then the probability that the ball was drawn from the first box is

1/2
6/7
4/7
3/7

Solution:

The total probability of the ball drawn to be black

= \frac{3}{6} \times \frac{3}{7} + \frac{3}{6} \times \frac{4}{7} = \frac{1}{2}

The probability of a black ball to be drawn from first box

= \frac{3}{6} \times \frac{3}{7} = \frac{3}{14}

Hence, by Baye's theorem, the probability that the ball

was drawn from the first box if the ball drawn is black

= \frac{\frac{3}{41}}{\frac{1}{2}} = \frac{3}{7}

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