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

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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 nos. 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﷯ Now, P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 2﷮36﷯﷮ 5﷮36﷯﷯ = 𝟐﷮𝟓﷯ ∴ Required probability is 2﷮5﷯

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