High School Binomial Probability Calculator
Calculate probability for n independent trials with success rate p.
Statistics
Calculated Probability
Distribution Graph
Understanding the Binomial Probability Calculator
The Binomial Distribution is one of the most important probability models in statistics. It describes the number of “successes” in a fixed number of independent trials, where each trial has only two possible outcomes: Success or Failure.
The BINS Conditions
To use the Binomial model, verify these four conditions:
- B: Binary outcomes (Success/Failure).
- I: Independent trials (one outcome doesn’t affect the next).
- N: Number of trials (n) is fixed.
- S: Success probability (p) is constant for each trial.
The Formula
The probability of getting exactly k successes in n trials is given by:
Where nCr or nCk represents the number of combinations (ways to choose the successes).
Why use a Binomial Probability Calculator?
Calculating “At least 5 successes” requires summing the probabilities for 5, 6, 7… up to n. This can be tedious to do by hand. This tool automates the cumulative summation and visualizes the distribution shape (skewed or symmetric), helping you understand the likelihood of events instantly.
FAQ
Yes, this tool is completely free for educational use.
“At most 3” means 0, 1, 2, or 3 successes. This is the cumulative probability P(X ≤ 3).
It handles standard high school problems (n up to 100-150) efficiently directly in the browser. Very large factorials may result in scientific notation.
Probabilities must be between 0 and 1. A value greater than 1 represents more than 100% chance, which is impossible.