Updated
Probability
Binomial Probability Calculator
Calculate exact binomial probabilities (P(X=k)), cumulative probabilities (≤ / ≥), inclusive ranges (a to b), and generate a distribution table with mean, variance and standard deviation.
Binomial Probability Tool
Enter trials (n) and success probability (p). Then choose a mode: exact, cumulative, range, or a table.
Exact probability uses P(X=k)=C(n,k)p^k(1−p)^(n−k). This is best when you need a precise answer (especially for small n or extreme p).
Cumulative probabilities add up multiple exact terms. Example: P(X ≤ k) sums P(0)+P(1)+…+P(k).
This tool also uses complements where helpful (like P(X ≥ k)=1−P(X ≤ k−1)).
Range probabilities are useful for “between” statements, like the probability of getting between 3 and 7 successes.
The full distribution has n+1 rows. For large n, generate a focused range (for example around the mean μ=np).