Binomial Probability
Calculator
Results
- Probability
- 0.250282
- Probability (%)
- 25.028228
- Number of combinations
- 120
Statistical results
| Probability | 0.250282 |
| Probability (%) | 25.028228 |
| Number of combinations | 120 |
formula-map diagram
- Probability
- 0.250282
- Probability (%)
- 25.028228
- Number of combinations
- 120
Statistical relationship
Formula
P(X = k) = C(n, k) × p^k × (1 − p)^(n − k)= 0.25028228759766
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What does a binomial probability calculation tell you?+
It gives the probability of getting exactly k successes in n independent trials, each with the same probability p of success. For example, the probability of flipping exactly 6 heads in 10 fair coin flips.
What conditions must be met to use the binomial formula?+
There must be a fixed number of trials, each trial must be independent, each trial has only two outcomes (success or failure), and the probability of success stays constant across all trials. If the probability changes between trials or trials aren't independent, the binomial model doesn't apply.
How is the formula constructed?+
It's C(n,k) × p^k × (1−p)^(n−k), where C(n,k) counts the number of ways to arrange k successes among n trials, p^k is the probability of those successes, and (1−p)^(n−k) is the probability of the remaining failures.
What's the difference between exact probability and cumulative probability?+
The core binomial formula gives the probability of exactly k successes, like exactly 3 heads. A cumulative probability, by contrast, sums that formula across a range, such as the probability of 3 or fewer heads, or of at least 5 heads.
Why does the probability sometimes surprise people for 'expected' outcomes?+
The single most likely outcome (like exactly 5 heads in 10 flips) often still has a fairly low probability on its own, because there are many other possible outcomes splitting the remaining probability. People often overestimate how likely the 'expected' or average result actually is.