Probability Basics: How to Find the Chance of an Event

Probability is a number from 0 to 1 that says how likely something is. 0 means impossible, 1 means certain, and 1/2 means as likely as a coin landing heads.

Try it with your own problem ↓

The steps

Decide what counts as a success, the event you are asking about.
List or count all the equally likely outcomes. This is the total.
Count the outcomes that make the event happen. These are the favorable outcomes.
Divide: probability = favorable ÷ total.
Simplify the fraction. You can also write it as a decimal or a percent.

A worked example

You roll two dice. What is the probability that the sum is 7?

Each die has 6 faces, so the total number of outcomes is 6 × 6 = 36.
List the ways to get 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). That is 6 favorable outcomes.
Probability = 6 ÷ 36.
Simplify: 6/36 = 1/6.

P(sum is 7) = 1/6, which is about 0.167 or 16.7%.

Try it with your own problem

Open the free The Chance Spinner with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: two dice sum of 7Opens The Chance Spinner with this example

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Common mistakes

Counting (3, 4) and (4, 3) as the same. They are different outcomes, because the dice are different.
Using the sums as outcomes. The sums 2 through 12 aren't equally likely, so use the 36 pairs.
Writing the probability as favorable ÷ unfavorable. That's the odds, not the probability.
Getting an answer bigger than 1. A probability is always between 0 and 1.

Questions people ask

What is the probability of an event not happening?

1 minus its probability. The chance of not rolling a 7 is 1 − 1/6 = 5/6.

What is the probability of two events both happening?

If they are independent, multiply them. Two heads in a row on a fair coin is 1/2 × 1/2 = 1/4.

What does a probability of 0.25 mean?

The event happens about 1 time in 4 over many tries. It does not guarantee any single try.

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