One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red.

One bag contains 3 red and 5 black balls. Another bag contains 6 red

Question 12 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 2
Question 12 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 3

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Question 12 (OR 1st question) One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red. 3 Red (R) 5 Black (B) 6 Red (R) 4 Black (B) Probability that ball drawn is red = Probability that ball transferred is red × Probability that red ball is picked from 2nd bag + Probability that ball transferred is black × Probability that red ball is picked from 2nd bag 3 Red (R) 5 Black (B) 6 Red (R) 4 Black (B) If red ball is transferred Probability that ball transferred is red = 3/8 Probability of getting a red ball from Bag II = 7/11 If black ball is transferred Probability that ball transferred is black = 5/8 Probability of getting a red ball from Bag II = 6/11 Thus, Probability that ball drawn is red = 3/8 × 7/11 + 5/8 × 6/11 = 21/88 + 30/88 = 51/88 Thus, required probability is 𝟓𝟏/𝟖𝟖

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.