Probability of obtaining at least k successes in n trials
🎲 Liars Dice: rolling at least k same faces among n dice
Number of trials (n):
Number of successes (k):
1's are wild
Binomial Probability Formula:
\( P(X = k) = \binom{n}{k} p^k (1 - p)^{n-k} \)
At Least k Successes Formula:
\( P(X \geq k) = \sum_{i=k}^{n} \binom{n}{i} p^i (1 - p)^{n-i} \)