Five Probability Calculator

Calculator form

Choose one of five probability methods and enter valid values.

Calculation type

Favorable outcomes

Total outcomes

Event probability P(A)

P(A)

P(B)

P(A ∩ B)

P(B)

Trials n

Successes k

Success probability p

Formula used

1) Simple event probability

P(E) = favorable outcomes / total outcomes

2) Complement probability

P(not A) = 1 - P(A)

3) Union of two events

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

4) Conditional probability

P(A | B) = P(A ∩ B) / P(B)

5) Binomial exact probability

P(X = k) = C(n, k) × p^k × (1 - p)^n-k

C(n, k) = n! / (k! × (n-k)!)

How to use this calculator

Select the probability method you need.
Enter only values that match that method.
Use decimals between 0 and 1 for probability inputs.
Click Calculate probability to show the result below the header.
Review the summary table and Plotly chart.
Download the output as CSV or PDF when needed.

Example data table

Method	Input example	Formula	Output
Simple event	favorable = 3, total = 10	P(E) = 3 / 10	0.3000
Complement	P(A) = 0.72	1 - 0.72	0.2800
Union	P(A)=0.55, P(B)=0.40, P(A∩B)=0.15	0.55 + 0.40 - 0.15	0.8000
Conditional	P(A∩B)=0.18, P(B)=0.30	0.18 / 0.30	0.6000
Binomial exact	n=8, k=3, p=0.25	C(8,3) × 0.25³ × 0.75⁵	0.369140625

Frequently asked questions

1. What does this calculator solve?

It solves five common probability tasks: simple event, complement, union, conditional, and exact binomial probability. Each method has separate inputs and its own summary output.

2. Should I enter percentages or decimals?

Enter probabilities as decimals between 0 and 1. For example, 60% should be entered as 0.60. The calculator converts the final answer into both decimal and percentage form.

3. When do I use complement probability?

Use complement when you know the chance of an event happening and need the chance it does not happen. The formula is simply 1 minus the event probability.

4. What is the difference between union and conditional probability?

Union measures the chance that at least one of two events occurs. Conditional probability measures the chance of one event assuming another event has already happened.

5. Why is the intersection needed for union?

Without subtracting the intersection, overlapping outcomes get counted twice. The intersection corrects that overlap and keeps the final union probability mathematically valid.

6. What does binomial exact probability mean?

It gives the chance of getting exactly k successes in n independent trials when every trial has the same success probability p. It is widely used in quality control and test scenarios.

7. Why can the calculator show validation errors?

Probability values must stay within logical limits. Inputs like probabilities above 1, negative counts, or intersections larger than their events are rejected to protect accuracy.

8. What does the chart help me understand?

The Plotly chart visualizes the result and its related components. For binomial mode, it shows the distribution shape. For other modes, it compares key probabilities directly.