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A die is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once? Select the correct answer from above options

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It is given that a die is thrown twice So the total outcome = 62 = 36 Consider P (A) as the probability of getting the number 5 at least once Consider P (B) as the probability of getting the sum = 8 Sample space of B = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)} P (B) = 5/36 Consider P (A ∩ B) as the probability of getting the number 5 at least once and the sum equal to 8 Sample space of (A ∩ B) = {(3, 5), (5, 3)} P (A ∩ B) = 2/36 = 1/18 Here the probability that the number 5 have appeared at least once given that the sum is 8

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