Mr. Vipin, a famous liar, is known to speak the truth 5 out of 6 times. His blind folded friend Shubham throws a pair of dice and asked Vipin the result, who says the sum of numbers on the pair of dice is 9 . The probability that the sum of

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Mr. Vipin, a famous liar, is known to speak the truth 5 out of 6 times. His blind folded friend Shubham throws a pair of dice and asked Vipin the result, who says the sum of numbers on the pair of dice is 9 . The probability that the sum of numbers on the pair of dice is actually 9 is k , then the value of 52 k is equal to

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Correct answer: 20

Let, A be an event that Vipin speaks the truth ⇒ P A = 5 6 and B be an event such that the sum on the pair of dice is equal to 9 ⇒ P B = 4 36 = 1 9 P B A = P B ∩ A P A = P B ⋅ P A B P B P A B + P B C P A c B c = 1 9 × 5 6 1 9 × 5 6 + 8 9 × 1 6 = 5 13

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