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Question
A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black?
Solution
There are 18 balls in the bag out of which two balls can be drawn in 18C2 ways.
So, total number of elementary events = 18C2 = 153
According to the question, both the balls drwan are either red or black, which means that the two balls should be of the same colour.
Out of five red balls, two red balls can be drawn in 5C2 ways.
Similarly, two black balls can be drawn from seven black balls in 7C2 ways.
So, favourable number of elementary events = 5C2 + 7C2 = 10 + 21 = 31
Hence, required probability = \[\frac{31}{153}\]
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