Ex 13.1, 10 - A black and a red dice are rolled. (b) Find conditional - Ex 13.1

part 2 - Ex 13.1, 10 (b) - Ex 13.1 - Serial order wise - Chapter 13 Class 12 Probability
part 3 - Ex 13.1, 10 (b) - Ex 13.1 - Serial order wise - Chapter 13 Class 12 Probability

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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.Our Sample Space is S = We need to find the Probability of obtaining the sum 8, given that the red die resulted in a number less than 4 Let E : Sum of numbers is 8 F : Number on red die is less than 4 We need to find P(E|F) Event E E = {(2, 6), (3, 5), (4, 4), (5, 6), (6, 2)} P(E) = 5/36 Event F F = {(1, 1), (2, 1), (3, 1), ………,(6, 1), (1, 2), (2, 2), ………………, (6, 2), (1, 3), (2, 3), ………………, (6, 3)} P(F) = 18/36 Also, E ∩ F = {(5, 3), (6, 2)} So, P(E ∩ F) = 2/36 Now, 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo