Probability of getting at least one double 1s when rolling two dice within 25 turns

Question

I'm trying to calculate the probability of rolling double 1s with 2 dice in 25 turns. My thought process was looking at the probability of the complement and then doing 1-P(Not getting both 1 on two dice).

The probability of not getting 1 on two dices is = $\frac{25}{36}$.

So I thought the probability of not getting at least 1 on both dices in 25 turns is $\left(\frac{{25}}{36}\right)^{25}$, but then subtracting this from 1 gives a very large number so it looks wrong. Can someone explain why, and perhaps give me your thought process on what you would do instead?

Answer 1

Out of the $36$ possible combinations, only one of them is the desired outcome.

The probability of getting $1$ on two dices is $\frac{1}{36}$.

Model it as $X\sim Bin(25,\frac1{36})$.

$P(X \ge 1)= 1-P(X=0)=1-(1-p)^{25}=1-(\frac{35}{36})^{25}$