Raffle with X participants. Same Raffle is repeated Y times. Odds of winning exactly/at least 1, 2, 3... times? There's a weekly raffle with 20 participants. It will last for 10 weeks. Every participant has the same probability of winning on any given week $\left(\frac1{20} \right)$. I know that the probability of me winning $0$ times is $\left(19\frac1{20} \right)^{10} = 59.9\%$, which means I have a $40.1\%$ chance of winning at least once, right? But how can I calculate the following probability: * Me winning exactly N times. * Me winning at least N times. Thanks,

Yes, you are right that the chance of winning at least once is about $40.1\%$. To calculate the probability to win exactly N times in $M$ weeks you have to use the binomial distribution.

$$P(X=N)=\binom{M}{N}\cdot \left(\frac{1}{20} \right)^{N}\cdot \left(\frac{19}{20} \right)^{M-N}$$

Similar for the probability to win at least $N$ times in $M$ weeks is

$$P(X\geq N)=\sum_{k=N}^{M}\binom{M}{k}\cdot \left(\frac{1}{20} \right)^{k}\cdot \left(\frac{19}{20} \right)^{M-k}$$