Probability Calculator

What Probability Measures

Probability (also called chance or likelihood) is just the share of outcomes you care about out of all the outcomes that could happen. Roll a die and you want a 4: there is one favorable outcome out of six possible, so the probability is $\tfrac{1}{6}$, about 16.67%. Every probability sits between 0 (impossible) and 1, or 0% and 100%.

This tool does three jobs. For a single event it turns favorable-out-of-total into a percentage, a simplified fraction, a decimal, and odds. For two independent events - ones that do not affect each other, like two separate coin flips - it combines their chances into the probability that both happen, that either happens, or that neither does. For one event repeated over multiple tries - the same chance again and again - it finds the probability it happens every time, at least once, or never.

How to Use It

1. Choose single event, two independent events, or one event repeated.
2. For a single event, enter the favorable and total outcomes.
3. For two events, enter the chance of each as a percentage.
4. For a repeated event, enter the chance each try and the number of tries.

The Formulas

For a single event:

$$P = \frac{\text{favorable outcomes}}{\text{total outcomes}}$$

For two independent events A and B:

$$P(\text{both}) = P(A) \times P(B) \qquad P(\text{either}) = P(A) + P(B) - P(A) \times P(B)$$

For one event with chance $p$ repeated over $n$ independent tries:

$$P(\text{every time}) = p^{\,n} \qquad P(\text{at least once}) = 1 - (1 - p)^{n}$$

Worked Examples

Question	Setup	Answer
Roll a 4 on a die	1 of 6	16.67%
Draw a heart from a deck	13 of 52	25%
Two coins both heads	50% and 50%, both	25%
Rain today or tomorrow (40% each)	40% and 40%, either	64%
At least one heads in 3 coin flips	50% each, 3 tries	87.5%

Independent vs Dependent Events

The “two events” mode assumes the events are independent - one happening does not change the odds of the other. Coin flips and separate dice are independent. Drawing two cards without replacing the first is not, because the deck changes, so those need a different calculation.