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  4. 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

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Q. 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 _____

JEE AdvancedJEE Advanced 2020

Solution:

Sum is perfect square if die's show $\{(1,3)(3,1)(2,2)(3,6)(6,3)(4,5)(5,4)\}$
so probability sum is $9$ when it is perfect square $p=4 / 7$
$14 \,p=8$