A pair of dice is thrown until the sum of numbers appeared is a perfect square or a non-perfect square sum appeared five times in succession. If random variable X denotes the number of non perfect square sums appeared then $P(X > 0)$ is

$\frac{29}{36}$

The correct answer is Option (2) → $\frac{29}{36}$ **

Event: X>0 ⇔ first roll is a non-perfect-square sum.

Perfect-square sums: 4 (3 outcomes), 9 (4 outcomes) ⇒ total 7 outcomes out of 36.

$P(X>0)=1-P(\text{perfect square on first roll})=1-\frac{7}{36}=\frac{29}{36}$