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Last updated at Feb. 15, 2020 by Teachoo
Example 8 An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black? We need to find probability that both balls drawn out are black Now, Probability both balls drawn are black = Probability first ball drawn is black Γ Probability second ball is black if first is black Finding both probabilities separately Probability first ball drawn is black There are 10 blacks balls out of 15 So, Probability = 10/15 = 2/3 Probability second ball drawn is black if first ball was black If first ball drawn was black, we are left with 9 black, 5 white balls So, Probability = (π ππππππππ π΅ππππ ππππ)/(π ππππππππ πππππ ) = 9/14 Therefore, Probability both balls drawn are black = Probability first ball drawn is black Γ Probability second ball is black if first is black = 2/3 Γ 9/14 = π/π
