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NDA Math Probability

Question : 78 of 100

Marks: +1, -0

Solution:

Consider the two given boxes

Box I → Red (2) Black(3)

Box II → Red (3) Black(2)

Probability of different colored balls in box 1 is

\frac{2 \times 3}{{}^{5}C_{2}} = \frac{6}{10} = \frac{3}{5}

Probability of different colored balls in box 2 is

\frac{3 \times 2}{{}^{5}C_{2}} = \frac{6}{10} = \frac{3}{5}

So if one box is chosen at random, the probability of different colored ball is

\frac{1}{2} \times \frac{3}{5} + \frac{1}{2} \times \frac{3}{5} = \frac{3}{5}

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