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Example 6 - A die is thrown twice, sum of numbers is 6. - Examples

Example 6 - Chapter 13 Class 12 Probability - Part 2
Example 6 - Chapter 13 Class 12 Probability - Part 3

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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 the sum of numbers is observed to be 6 Let F : Sum of numbers is 6 E : 4 Has appeared at least once We need to find P(E|F) Also, E ∩ F = {(2, 4), (4, 2)} P(E ∩ F) = 2/36 Let F : Sum of numbers is 6 E : 4 Has appeared at least once We need to find P(E|F) Also, E ∩ F = {(2, 4), (4, 2)} P(E ∩ F) = 2/36 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 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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.