Two fair dice, each with faces numbered 1 , 2 , 3 , 4 , 5 and 6 , are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime numbe

Question

Two fair dice, each with faces numbered 1 , 2 , 3 , 4 , 5 and 6 , are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns out to be a perfect square before it turns out to be a prime number. If p is the probability that this perfect square is an odd number, then the value of 14 p is_____

TestHub · Accepted Answer

Perfect Square can be 4 or 9 , which can be obtained by 1 , 3 , 3 , 1 , 2 , 2 , 6 , 3 3 , 6 , 5 , 4 , 4 , 5 . Prime Number can be 2 or 3 or 5 or 7 or 11 , which can be obtained by 1 , 1 , 1 , 2 , 2 , 1 , 1 , 4 , 4 , 1 , 2 , 3 , 3 , 2 , 1 , 6 , 6 , 1 , 5 , 2 , 2 , 5 , 3 , 4 , 4 , 3 , 6 , 5 , 5 , 6 P (square or prime) = 22 36 P Perfect square is odd perfect square before prime = 4 36 + 14 36 . 4 36 + 14 36 . 14 36 . 4 36 + . . . . 7 36 + 14 36 . 7 36 + 14 36 . 14 36 . 7 36 + . . . . . . = 4 36 1 - 14 36 7 36 1 - 14 36 = 4 7 = P ⇒ 14 P = 8

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