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_____

Step-by-step solution

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 + . .