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Question
A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that one ball is black and the other red
Solution
Out of 16 balls, two balls can be drawn in 16C2 ways.
∴ Total number of elementary events = 16C2 = 120
Out of five black balls, one black ball can be drawn in 5C1 ways.
Out of four red balls, one red ball can be drawn in 4C1 ways.
Therefore, one black and one red balls can be drawn in 5C1× 4C1 ways.
∴ Favourable number of ways = 5C1× 4C1 = 5× 4 = 20
Hence, required probability = \[\frac{20}{120} = \frac{1}{6}\]
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