Probability Calculator
Our Probability Calculator helps you quickly calculate the likelihood of different outcomes using the binomial probability formula. Whether you want to find the probability of exactly x successes, at least x successes, at most x successes, or even the probability within a range, this tool gives you instant, step-by-step solutions.
What is Probability?
Probability is a measure of how likely an event is to occur. It ranges from 0 (impossible) to 1 (certain). For example, flipping a fair coin has a probability of 0.5 (50%) for heads and 0.5 for tails.
In real-life, probability is widely used in:
Business & Finance – risk assessment, forecasting
Health & Science – medical trial outcomes, genetics
Education & Exams – understanding likelihood of test results
Sports & Games – predicting match outcomes, gambling strategies
How This Calculator Works
This calculator uses the binomial distribution to determine probabilities. The formula is:
P(X=k)=(nk)×pk×(1−p)n−kP(X = k) = \binom{n}{k} \times p^k \times (1-p)^{n-k}
Where:
n = total number of trials
k = number of successful events
p = probability of success in a single trial
Features of Our Probability Calculator:
Calculate the probability of exactly x successes
Find the probability of at least x successes
Determine the probability of at most x successes
Compute probability within a given range
Get step-by-step calculations with substitution and results
Clean and mobile-friendly interface
This makes it easy for students, teachers, professionals, and anyone curious about probability to calculate outcomes with accuracy.
Example
If you flip a fair coin 10 times, what is the probability of getting exactly 3 heads?
The calculator shows:
P(X=3)=(103)×(0.5)3×(0.5)7=0.1172 (11.72%)P(X=3) = \binom{10}{3} \times (0.5)^3 \times (0.5)^7 = 0.1172 \, (11.72\%)