How to calculate probability
Probability measures how likely an event is, on a scale from 0 to 1. This guide shows the basic formula, a step-by-step method, and how to combine events for and and or questions.
The basic formula
For a situation where every outcome is equally likely, the probability of an event is the number of favorable outcomes divided by the total number of outcomes. Rolling an even number on a die is 3 favorable outcomes out of 6, so the probability is 0.5. The answer always lands between 0 and 1.
Step by step
- Count the total number of equally likely outcomes.
- Count how many of those count as your event.
- Divide the favorable count by the total.
- Multiply by 100 if you want a percentage.
Drawing a heart from a 52-card deck: 13 hearts out of 52 cards, so 13 / 52 = 0.25, or 25 percent.
Combining events
For two events, multiply when you want both to happen (and) and they are independent, and add when you want either one (or), subtracting any overlap. The probability an event does not happen is 1 minus the probability it does. These three moves handle most everyday probability questions.
- Probability = favorable outcomes / total outcomes, between 0 and 1.
- Count the total outcomes and the favorable ones, then divide.
- Multiply by 100 to express it as a percentage.
- For both events (and), multiply independent probabilities.
- For either event (or), add and subtract the overlap.
Related references
Use the Probability Calculator, the Probability Formula, or the Probability Rules.
FAQ
How do I calculate the probability of an event?
Divide the number of favorable outcomes by the total number of equally likely outcomes.
What is the probability of rolling a 6 on a die?
1 out of 6, about 0.167 or 16.7 percent.
How do I find the probability of two events both happening?
For independent events, multiply their individual probabilities.