Question bank/JEE Advanced/Mathematics

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 what is the value of $14 p$?

Source: JEEBench (IIT Delhi) / JEE Adv 2020 Paper 2