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Ex 13.5, 2 - A pair of dice is thrown 4 times. Getting doublet - Binomial Distribution

Ex 13.5, 2 - Chapter 13 Class 12 Probability - Part 2
Ex 13.5, 2 - Chapter 13 Class 12 Probability - Part 3

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Ex 13.5, 2 A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes. Let X : be the number of doublets Throwing a pair of die is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒﷮𝒏−𝒙﷯ 𝒑﷮𝒙﷯ Where n = number of times die is thrown = 4 Finding p, q If 2 dies are thrown, there are 6 × 6 = 36 outcomes Doublet: It means same number is obtained on both throws of die Number of doublets possible on 2 throws of die are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) P(getting a doublet) = p = 6﷮36﷯ = 1﷮6﷯ P(not getting a doublet) = q = 1 – 1﷮6﷯ = 5﷮6﷯ Hence, P(X = x) = 4Cx 𝟏﷮𝟔﷯﷯﷮𝒙﷯ 𝟓﷮𝟔﷯﷯﷮𝟒 − 𝒙﷯ We need to find probability of two successes. P(getting two successes) = P(getting 2 doublets) = P(X = 2) = 4C2 1﷮6﷯﷯﷮2﷯ 5﷮6﷯﷯﷮4 −2﷯ = 4!﷮ 4 − 2﷯! 2!﷯ 1﷮6﷯﷯﷮2﷯ 5﷮6﷯﷯﷮2﷯ = 4 × 3 × 2!﷮2! × 2!﷯ 1﷮6﷯﷯﷮2﷯ 5﷮6﷯﷯﷮2﷯ = 2 × 3 × 1﷮6 × 6﷯ × 25﷮36﷯ = 𝟐𝟓﷮𝟐𝟏𝟔﷯

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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.