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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. Probability first ball is black and second ball is red Probability first ball is black = 5/(5 + 5) = 5/10 = 1/2 Now, there are 5 Red and (5 + 2 =) 7 Black balls in the urn. So, Probability second ball is red, when first ball is black = 5/(5 +7) = 𝟓/𝟏𝟐 Probability first ball is red and second ball is red Probability first ball is red = 1 − P(first is black) = 1 − 1/2 = 1/2 Now, there are (5 + 2 =) 7 Red and 5 Black balls in the urn So, Probability second ball is red, when first ball is red = 7/(5 + 7) = 𝟕/𝟏𝟐 Thus, 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. = 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 𝟏/𝟐

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.