What Is Find Probability?
To find a probability you first choose the distribution that models your situation, then compute the area or sum that matches your question, such as P(X < x), P(X > x), P(X = x) or P(a ≤ X ≤ b).
Pick the distribution, enter its parameters and the value x, and the calculator returns the probability and its complement, the mean and standard deviation, and a chart with the region highlighted. For discrete distributions it distinguishes < from ≤; for continuous ones it explains that a single value has probability zero.
The article below includes a table to help you choose the right distribution, the key formulas, worked examples and common questions.
How to Use the Find Probability Calculator
- Pick the distribution and enter its parameters.
- Choose the type of probability.
- Enter x (and x₂ for a range).
- Read the probability and its complement and check the chart.
Find Probability Formula
Range probability
Upper tail
Standardising (normal)
Find Probability Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| X | The random variable | |
| x | The value in your question | |
| F(x) | Cumulative probability P(X ≤ x) | |
| Parameters | μ, σ, n, p, λ, a, b or df | depend on the distribution |
Find Probability Worked Example
With the example values loaded in the calculator above, the steps are:
- Model: Normal(100, 15²).
- P(X ≤ 115) = 0.84134475.
- For a continuous distribution P(X < x) = P(X ≤ x), because single points have zero probability.
Result: P(X ≤ 115) = 0.84134475.
Worked example
For scores with mean 100 and SD 15, P(X ≤ 115) = Φ((115 − 100) ÷ 15) = Φ(1) = 0.8413. For a binomial with n = 20 and p = 0.3, P(X ≤ 6) = 0.6080.
Where Find Probability Is Used
Probability homework
Checking answers across several distributions.
Quick what-if questions
Finding the chance of an event under a model.
Comparing models
Seeing how the same x behaves under different distributions.
Teaching
Showing tails, ranges and complements.
Common Find Probability Mistakes to Avoid
- Discrete distributions distinguish < from ≤; continuous ones do not.
- Check parameters carefully; a rate and a mean are not the same thing.
- Use the complement for "at least" questions.
Find Probability Terms and Definitions
- CDF
- The cumulative distribution function F(x) = P(X ≤ x).
- PMF
- The probability mass function for a discrete variable.
Find Probability FAQs
How do I find a probability?
Identify the distribution, enter its parameters, and compute the area or sum that matches your question.
How do I find the probability between two values?
Subtract the cumulative probability at the lower value from that at the upper value.
What is the probability of exactly one value?
Zero for continuous variables; use the PMF for discrete ones.
How do I find "at least" probability?
Use 1 − P(X < x) (for discrete) or 1 − P(X ≤ x) (continuous).