Probability calculator

How basic probability works

Probability measures how likely an event is, expressed as a number between 0 and 1, or as a percentage between 0% and 100%. The basic formula is straightforward: divide the number of favorable outcomes by the number of total possible outcomes.

Worked example: a standard six-sided die has 6 total outcomes. Rolling an even number has 3 favorable outcomes (2, 4 and 6), so the probability is 3/6, which simplifies to 1/2, or 50%. Drawing an ace from a standard 52-card deck has 4 favorable outcomes out of 52 total, giving a probability of 4/52, which simplifies to 1/13, or about 7.7%.

Simplifying the fraction makes the result easier to read and compare. The calculator above does this automatically by finding the greatest common divisor of the favorable and total outcomes and dividing both numbers by it.

AND vs OR for combined events

When you want the probability of two events happening together or of either one happening, the formula depends on how the events relate to each other. This calculator covers the two simplest and most common cases.

• AND, for independent events: multiply the two probabilities. If flipping a coin gives 50% heads and rolling a die gives a 1/6 chance of a six, the probability of both happening is 0.5 × (1/6), or about 8.3%. Independent means the outcome of one event does not affect the other.
• OR, for mutually exclusive events: add the two probabilities. If a bag has a 30% chance of drawing red and a 20% chance of drawing blue, and a marble cannot be both colors, the probability of drawing red or blue is 30% + 20%, or 50%. Mutually exclusive means the two events cannot both happen at once.

These formulas only hold under those specific conditions. If two events are dependent, meaning one influences the probability of the other, the AND formula needs to account for that changed probability instead of simply multiplying the original two numbers. If two events can overlap rather than being mutually exclusive, the OR formula needs to subtract the probability of both happening together, to avoid double-counting. This calculator intentionally sticks to the simple independent and mutually exclusive cases and does not attempt the general formulas.

Where basic probability shows up in everyday life

Basic probability is most useful for games of chance and simple risk estimates, where outcomes are clearly defined and roughly equally likely, such as card games, dice, coin flips, or raffle drawings. It can also help with quick, rough estimates, like weighing the odds of two independent random events both going your way.

For anything involving real-world statistics with messy, dependent, or overlapping factors, such as medical test results, weather forecasting, or financial risk, the simple formulas here are a starting point at best. Those situations typically call for more advanced statistical tools that properly account for dependence and correlation between events.

Frequently asked questions

How do I calculate basic probability?

Divide the number of favorable outcomes by the number of total possible outcomes. For example, rolling a 4 or higher on a six-sided die has 3 favorable outcomes out of 6 total, so the probability is 3/6, which simplifies to 1/2, or 50%.

What is the difference between AND and OR in probability?

For independent events, AND means both events happen, calculated by multiplying their probabilities. For mutually exclusive events, OR means either one happens, calculated by adding their probabilities.

Does this calculator handle dependent events?

No. The combined probability mode here assumes events are independent for AND and mutually exclusive for OR. Real-world events are sometimes dependent, where one event affects the other's probability, or overlapping, where both can happen together, which requires different formulas not covered by this tool.

Can probability be greater than 100%?

No. A valid probability is always between 0% and 100%. If your inputs for combined OR probability add up to more than 100%, double check that the events are actually mutually exclusive, since this simple formula assumes they cannot both happen.

Why is my fraction simplified differently than I expected?

The calculator reduces the fraction of favorable to total outcomes to its lowest terms using the greatest common divisor. For example, 2 favorable out of 6 total simplifies to 1 out of 3, since 2 is the greatest common divisor of 2 and 6.