Probability of rolling a specific number on a dice 2+ times in x throws

Question

Would need help with a probability calculations question

if I have a 25 face dice and I roll it 62 times, what is the probability that at least 2 times I roll a 5? How about If I roll it 30 times?

What's the actual formula for calculating the probability of rolling a specific number on a dice 2+ times in x throws?

Edit:

1. So if this is the correct formula $\binom{n}{k}p^kq^{n−k}$, what would represent $n$, $k$, $p$, $q$ in my situation? Sorry, it's been 20 years since I've graduated Uni, and haven't used these formulas since, so they are a foreign language now.

Answer 1

You have found the right formula, yes. To be precise, the probability of rolling $5$ on a $25$-sided die at least $2$ times in $n$ throws is $\sum_{k=2}^{n}\binom{n}{k}(\frac{1}{25})^k(\frac{24}{25})^{n-k}$. Matching terms in this expression with those of your formula answers the questions posed in your edit: $n$ represents the total number of times you toss the die, $k$ represents the number of "successes" ("success" defined here as rolling a $5$) you wish to calculate the probability of, $p$ represents the raw probability of success ($1$ in $25$) and $q$ represents the probability of failure.