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Short answer
Binompdf(n, p, k) returns the exact probability P(X = k), while binomcdf(n, p, k) returns the cumulative probability P(X ≤ k). In Excel use BINOM.DIST with FALSE for exact and TRUE for cumulative.
1. The difference
- PDF / PMF: the probability of exactly k successes, P(X = k).
- CDF: the probability of k or fewer successes, P(X ≤ k).
2. Syntax
| Tool | P(X = k) | P(X ≤ k) |
|---|---|---|
| TI-83 / TI-84 | binompdf(n, p, k) | binomcdf(n, p, k) |
| Excel, Google Sheets | =BINOM.DIST(k, n, p, FALSE) | =BINOM.DIST(k, n, p, TRUE) |
| R | dbinom(k, n, p) | pbinom(k, n, p) |
| Python (SciPy) | binom.pmf(k, n, p) | binom.cdf(k, n, p) |
3. Example: n = 10, p = 0.5, k = 3
| Result | Value |
|---|---|
| P(X = 3) | 0.117188 |
| P(X ≤ 3) | 0.171875 |
| P(X ≥ 4) | 0.828125 |
4. Other questions from the same functions
- At least k: 1 − binomcdf(n, p, k − 1).
- Between a and b: binomcdf(n, p, b) − binomcdf(n, p, a − 1).
- Less than k: binomcdf(n, p, k − 1).
The Binomial Probability Calculator shows P(X = k), P(X ≤ k), P(X ≥ k), P(X < k) and P(X > k) together, so you can check your calculator or spreadsheet result. Formula background: how to calculate binomial probability.
5. Frequently asked questions
What is the difference between binompdf and binomcdf?expand_more
binompdf gives the exact probability P(X = k). binomcdf gives the cumulative probability P(X ≤ k).
How do I do binomcdf in Excel?expand_more
Use =BINOM.DIST(k, n, p, TRUE).
How do I find at least k with binomcdf?expand_more
Use 1 − binomcdf(n, p, k − 1).
What is binompdf(10, 0.5, 3)?expand_more
0.117188.