Probability formula
The basic probability formula gives the chance of an event as the number of favorable outcomes divided by the total number of equally likely outcomes. The result runs from 0 (impossible) to 1 (certain).
- P(E) = the probability of event E, between 0 and 1
- favorable outcomes = the number of outcomes that count as the event
- total outcomes = the number of all equally likely outcomes
Reading a probability
A probability of 0 means the event cannot happen, 1 means it is certain, and 0.5 means it is equally likely to happen or not. Multiplying by 100 converts it to a percentage. The formula assumes every outcome is equally likely, as with a fair die or a well-shuffled deck.
Combining events
For independent events, the probability that both A and B happen is P(A) times P(B). The probability that A or B happens is P(A) plus P(B) minus the overlap P(A and B). These rules build more complex probabilities from the basic formula.
- Roll a fair six-sided die and ask for the probability of an even number.
- Favorable outcomes: 2, 4, 6, which is 3 outcomes.
- Total outcomes: 6.
- P(even) = 3 / 6 = 0.5, or 50 percent.
Calculate odds
Use the Probability Calculator, or read the Normal Distribution Guide for probabilities on the bell curve.
FAQ
What is the basic probability formula?
P(E) = favorable outcomes / total outcomes, assuming all outcomes are equally likely. The result is between 0 and 1.
How do I find the probability of two events both happening?
For independent events, multiply their probabilities: P(A and B) = P(A) × P(B).