Example 6 - Chapter 13 Class 12 Probability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 and Computer Science at Teachoo