Ex 13.3, 1 - Chapter 13 Class 12 Probability

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Ex 13.3, 1 An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red? Let B : first ball drawn is black R : second ball is red Probability that the second ball is red = Probability that the first ball is black Probability that the second ball is red if first is black + Probability that first ball is red Probability that second ball is red if first is red. P(R) = P(B) . P(R|B) + P(B ) . P(R|B ) Putting above values in (1), P(R) = P(B) . P(R|B) + P(B ) . P(R|B ) = 1 2 5 12 + 1 2 7 12 = 5 24 + 7 24 = 12 24 = 1 2 Therefore, Probability that the second ball is red is