Binomial Distribution Calculator
Find binomial probabilities: exactly, fewer than, at most, more than and at least x successes in n trials, with the mean and standard deviation.
Change the values and press Calculate to work out your own figures.
Enter the chance of success, the number of trials and the number of successes.
Show the working
- P(X = x) = C(n, x) × p^x × (1 − p)^(n − x)
- = C(10, 3) × 0.5^3 × 0.5^7 = 0.1171875
How to use it
Enter the chance of success, the number of trials and the number of successes.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
P(X = x) = C(n, x) pˣ (1 − p)ⁿ⁻ˣ
When to use it
A binomial distribution fits a fixed number of independent yes/no trials with the same chance of success each time, such as flipping a coin 10 times.
Questions
What is the probability of exactly 3 heads in 10 flips?
120 ÷ 1024 = 0.1171875.
What is the mean of a binomial distribution?
n × p.
Formulas
P(X = x) = C(n, x) pˣ (1 − p)ⁿ⁻ˣ
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).