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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 both the balls are of the same colour.
Solution
Out of 16 balls, two balls can be drawn in 16C2 ways.
∴ Total number of elementary events = 16C2 = 120
'Two balls drawn are of the same colour' means that both are either white or black or red.
Out of seven white balls, two white balls can be drawn in 7C2 ways.
Similarly, two black balls can be drawn from five black balls in 5C2 ways and two red balls can be drawn from four red balls in 4C2 ways.
Therefore, number of ways of drawing two balls of the same colour = 7C2 + 5C2 + 4C2 = 21 + 10 + 6 = 37
i.e. favourable number of ways = 37
Hence, required probability = \[\frac{37}{120}\]
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