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Probability Calculator

Find the probability of two independent events both happening, either happening, exactly one or neither; solve for the events from any two probabilities; or find the chance of a series of repeated events.

Change the values and press Calculate to work out your own figures.

Two independent events

Enter P(A) and P(B) for two independent events.

Probability of event A: 0.3, 3/10 or 30%.
Probability of event B.
Result
P(A ∩ B), both
0.2
P(A ∪ B), A or B or both
0.7
P(A Δ B), exactly one
0.5
P((A ∪ B)′), neither
0.3
P(A′), not A
0.5
P(B′), not B
0.6
P(A and not B)
0.3
P(B and not A)
0.2

For independent events with P(A) = 0.5 and P(B) = 0.4, both happen with probability 0.2.

Show the working
  1. P(A ∩ B) = P(A) × P(B) = 0.5 × 0.4 = 0.2
  2. P(A ∪ B) = P(A) + P(B) − P(A ∩ B) = 0.7
  3. P(A Δ B) = P(A ∪ B) − P(A ∩ B) = 0.5
  4. P(neither) = (1 − P(A)) × (1 − P(B)) = 0.3

Solve from any two probabilities

Enter any two of the eight probabilities to work out the rest (independent events).

Probability of event A: 0.3, 3/10 or 30%.
Probability of event B.
Probability that A doesn't happen.
Probability that B doesn't happen.
Probability that both happen.
Probability that A or B or both happen.
Probability that exactly one happens.
Probability that neither happens.
Result
P(A) and P(B)
0.5 and 0.4
P(A ∩ B), both
0.2
P(A ∪ B), A or B or both
0.7
P(A Δ B), exactly one
0.5
P((A ∪ B)′), neither
0.3
P(A′), not A
0.5
P(B′), not B
0.6
P(A and not B)
0.3
P(B and not A)
0.2

Independent events with those probabilities have P(A) = 0.5 and P(B) = 0.4.

Show the working
  1. Solve for P(A) and P(B), assuming A and B are independent
  2. P(A) = 0.5, P(B) = 0.4

Series of repeated events

Enter each event's probability and how many times it is repeated.

Probability of event A: 0.3, 3/10 or 30%.
How many independent tries of A.
Probability of event B.
How many independent tries of B.
Result
A every one of 5 times
0.07776
A never happens in 5 tries
0.01024
A happens at least once
0.98976
B every one of 3 times
0.027
B never happens
0.343
B happens at least once
0.657
A every time and B every time
0.00209952
Neither A nor B ever happens
0.00351232

A happens all 5 times with probability 0.07776.

Show the working
  1. P(A every time) = 0.6^5 = 0.07776
  2. P(A at least once) = 1 − (1 − 0.6)^5

How to use it

Enter P(A) and P(B) for two independent events. Enter any two of the eight probabilities to work out the rest (independent events). Enter each event's probability and how many times it is repeated.

Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.

Key facts

P(A ∩ B) = P(A) P(B) (independent)
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A′) = 1 − P(A)

Independent events

Two events are independent when one happening doesn't change the chance of the other, like two coin flips. The formulas here assume independence; for dependent events use conditional probabilities and Bayes' theorem.

Questions

What is the probability of both events happening?

For independent events, multiply: 0.5 × 0.4 = 0.2.

How do I enter 30%?

Type 0.3, 3/10 or 30%.

Reviewed by RK Calculator Team. Updated 2026-09-26.

Formulas

P(A ∩ B) = P(A) P(B) (independent)
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A′) = 1 − P(A)

Sources

Limitations

  • Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).

Formula version 0.1.0Reviewed