Example 6 - Chapter 13 Class 12 Probability (Important Question)

Last updated at April 16, 2024 by Teachoo

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Example 6 A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once? A dice is thrown twice S = We need to find the Probability that 4 has appeared at least once, given that the sum of numbers is observed to be 6 Let E : 4 Has appeared at least once F : Sum of numbers is 6 We need to find P(E|F) Event E E = {(1, 4), (2, 4), (3, 4), (4, 4), (5, 4), (6, 4), (4, 1), (4, 2), (4, 3), ,(4, 5), (4, 6)} P(E) = 11/36 Event F F = {(1, 5), (5, 1), (2, 4), (4, 2), (3, 3)} P(F) = 5/36 Now, P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹)) = (2/36)/(5/36) = 𝟐/𝟓 ∴ Required probability is 2/5 Also, E ∩ F = {(2, 4), (4, 2)} P(E ∩ F) = 2/36

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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