Want to find the probability of an event? Our free Probability Calculator makes it easy to calculate the chance of something happening. Enter the number of favorable outcomes and the total number of possible outcomes to get the probability as a fraction, decimal, and percentage.
Probability Calculator
How to Use the Probability Calculator
Using the Probability Calculator is simple. Enter the number of favorable outcomes and the total number of possible outcomes, then click Calculate Probability.
The calculator will show the probability as a decimal, simplified fraction, and percentage.
For example, if there are 2 favorable outcomes out of 6 possible outcomes, enter 2 as the favorable outcomes and 6 as the total outcomes.
What Is Probability?
Probability is a way of describing how likely an event is to happen.
It is usually expressed as a number between 0 and 1, a fraction, or a percentage.
A probability of 0 means an event cannot happen, while a probability of 1 means the event is certain to happen.
Probability Formula
The basic probability formula is:
Probability = Favorable Outcomes ÷ Total Possible Outcomes
For example, if there are 3 favorable outcomes out of 10 possible outcomes:
3 ÷ 10 = 0.3
So the probability is:
0.3 = 30% = 3/10
Understanding Probability
Probability values can be understood in a few simple ways:
- 0 means the event is impossible.
- Between 0 and 1 means the event has some chance of happening.
- 1 means the event is certain.
- A higher probability means the event is more likely to occur.
- A lower probability means the event is less likely to occur.
Probability Examples
Example 1: Rolling a Die
A standard six-sided die has six possible outcomes: 1, 2, 3, 4, 5, and 6.
The probability of rolling a 4 is:
1 ÷ 6 = 1/6
As a percentage, this is approximately 16.67%.
Example 2: Drawing a Red Ball
Suppose a bag contains 10 balls, and 4 of them are red.
The probability of randomly picking a red ball is:
4 ÷ 10 = 2/5
That is equal to 0.4 or 40%.
Example 3: Tossing a Coin
A standard coin has two possible outcomes: heads or tails.
The probability of getting heads is:
1 ÷ 2 = 1/2
That is equal to 0.5 or 50%.
Probability as a Fraction, Decimal and Percentage
The same probability can be written in different forms.
For example:
1/4 = 0.25 = 25%
These values all represent the same probability.
The calculator displays all three forms so you can use whichever format is more convenient.
The Difference Between Probability and Odds
Probability and odds are related, but they are not the same thing.
Probability compares favorable outcomes with all possible outcomes.
Odds compare favorable outcomes with unfavorable outcomes.
For example, if there is 1 favorable outcome and 3 unfavorable outcomes:
- Probability = 1/4 = 25%
- Odds in favor = 1:3
Frequently Asked Questions
What is the probability formula?
The basic formula is Probability = Favorable Outcomes ÷ Total Possible Outcomes.
Can probability be greater than 1?
For a standard probability, no. A probability is between 0 and 1, inclusive, or between 0% and 100%.
What does a probability of 0 mean?
A probability of 0 means the event is impossible under the conditions being considered.
What does a probability of 1 mean?
A probability of 1 means the event is certain to happen under the conditions being considered.
Can probability be written as a percentage?
Yes. Multiply the decimal probability by 100 to convert it into a percentage.
What is a 50% probability?
A 50% probability means the event has a one-half chance of occurring when the stated probability model applies.
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