Probability Calculator

Enter the probability of two events to see the chance of both, either or neither.

%
%
For the chance of A happening at least once in repeated tries

Results

Both A and B
15%
A or B (at least one)
65%
Exactly one of them
50%
Neither
35%
A but not B
35%
Not A
50%
A at least once in 5 tries
96.88%
A every time in 5 tries
3.13%

The calculation assumes A and B are independent events.

Probability expresses the chance of an event as a number between 0 and 1, or 0% and 100%. If two events do not affect each other they are independent, and the chance of both is the product of the two.

Intuition often gets this wrong: two events with a 50% and a 30% chance happen together only 15% of the time. In repeated tries, on the other hand, small chances grow quickly.

How to calculate Probability

  1. Enter the probability of event A as a percentage.
  2. Enter the probability of event B.
  3. Enter a number of tries for A to see the chance of it happening at least once.

Probability formula

  • P(A and B) = P(A) × P(B)
  • P(A or B) = P(A) + P(B) − P(A) × P(B)
  • P(neither) = (1 − P(A)) × (1 − P(B))
  • At least once in n tries: 1 − (1 − P(A))ⁿ

Probability example

With A at 50% and B at 30%, the chance of both is 15%, of at least one 65% and of neither 35%. A 50% event happens at least once in 5 tries 96.88% of the time.

Probability: common questions

What is an independent event?

One whose outcome does not affect the other — two separate dice rolls, for example. Cards drawn one after another from the same deck are dependent.

After five heads in a row, is tails more likely?

No. Each flip is independent and the chance stays 50%. Believing otherwise is the gambler’s fallacy.

Are probability and odds the same?

No. Probability is favourable outcomes over all outcomes; odds are favourable over unfavourable. A 25% probability is odds of 1 to 3.