Ex 13.1, 10 (b) - 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