Ex 13.1, 10 (a) - Chapter 13 Class 12 Probability

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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 9, given that the black die resulted in a 5.Since both dies are rolled S = We need to find the Probability of obtaining a sum greater than 9, given that the black die resulted in 5 Let E : Sum of numbers greater than 9 F : 5 appeared on the black die We need to find P(E|F) Event E E = {(4, 6), (5, 5), (6, 4), (5, 6), (6, 5) , (6, 6)} P(E) = 6/36 Event F F = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)} P(F) = 6/36 Also, E ∩ F = {(5, 5), (5, 6)} So, P(E ∩ F) = 2/36 Now, P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹)) = (2/36)/(6/36) = 2/6 = 𝟏/𝟑 ∴ Required probability is 1/3