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  1. Class 12
  2. Important Question for exams Class 12
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Ex 13.1, 10 A black and a red dice are rolled. (a) Find the conditional probability of obtaining a sum greater than 4, given that the black die resulted in a 5. A black and a red dice are rolled Let us take first numbers to have been appeared on the black die and the second numbers on the red die, in order. S = {(1,1), ……….., (1,6), (2,1), ………, (2,6), (3,1), ………., (3,6), (4,1), ……...., (4,6), (5,1), …….., (5,6), (6,1), …..…., (6,6)} We need to find the probability of obtaining a sum greater than 4, given that the black die resulted in 5 F : 5 appeared on the black die E: Sum of numbers greater than 4 We need to find P(E|F) Also, E ∩ F = {(5,5), (5,6)} So, P(E ∩ F) = 2﷮36﷯ = 1﷮18﷯ P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 2﷮36﷯﷮ 6﷮36﷯﷯ = 2﷮6﷯ = 1﷮3﷯ ∴ Required probability is 1﷮3﷯ Ex 13.1, 10 A black and a red dice are rolled. (b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4. We need to find the probability of obtaining the sum 8, given that the red die resulted in a number less than 4 F : number on red die is less than 4 E : sum of numbers is 8 We need to find P(E|F) Also, E ∩ F = {(5, 3), (6, 2)} So, P(E ∩ F) = 2﷮36﷯ P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 2﷮36﷯﷮ 18﷮36﷯﷯ = 2﷮18﷯ = 𝟏﷮𝟗﷯ ∴ Required probability is 1﷮9﷯

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.