Probability Calculator
A probability calculator helps determine how likely an event is to occur. Probability is used in mathematics, statistics, games, risk analysis, science, finance, and everyday decision-making.
What Is Probability?
Probability is a measure of the chance that an event will happen. It ranges from 0 to 1, or from 0% to 100%.
A probability of 0 means an event is impossible, while a probability of 1 means the event is certain to occur.
Basic Probability Formula
When all possible outcomes are equally likely, the probability of an event is:
P(E) = Favorable Outcomes Γ· Total Possible Outcomes
For example, a standard six-sided die has six possible outcomes. The probability of rolling a 4 is:
P(4) = 1 Γ· 6 β 0.1667
As a percentage, this is approximately 16.67%.
Probability of an Event Not Happening
The probability that an event does not occur is called its complement. It can be found using:
P(not E) = 1 β P(E)
For example, if the probability of rain is 30%, the probability of no rain is:
100% β 30% = 70%
Probability of Two Independent Events
When two events are independent, the probability that both occur is found by multiplying their individual probabilities:
P(A and B) = P(A) Γ P(B)
For example, the probability of getting heads on two independent coin tosses is:
1/2 Γ 1/2 = 1/4 = 25%
Probability of Either Event Occurring
For two events, the probability that at least one occurs can be calculated using:
P(A or B) = P(A) + P(B) β P(A and B)
The final subtraction prevents the outcomes common to both events from being counted twice.
Simple Probability Examples
| Situation | Probability |
|---|---|
| Rolling a 6 on a fair die | 1/6 β 16.67% |
| Getting heads on a fair coin | 1/2 = 50% |
| Rolling an even number on a fair die | 3/6 = 50% |
| Rolling a number greater than 4 on a fair die | 2/6 β 33.33% |
Theoretical vs. Experimental Probability
Theoretical probability is calculated from the possible outcomes of an event. Experimental probability is based on what actually happens during repeated trials.
For example, a fair coin has a theoretical probability of 50% for heads. If you toss the coin 20 times and get heads 12 times, the experimental probability is:
12 Γ· 20 = 0.60 = 60%
Experimental results may differ from theoretical probability, especially when the number of trials is small.
Probability as a Fraction, Decimal, or Percentage
A probability can be expressed in different forms. For example:
1/4 = 0.25 = 25%
To convert a probability from a decimal to a percentage, multiply it by 100.
Common Mistakes to Avoid
Make sure the total number of possible outcomes includes every relevant outcome and that the outcomes are equally likely before using the basic favorable-outcomes formula.
Also remember that a probability cannot be less than 0 or greater than 1. When expressed as a percentage, it must be between 0% and 100%.
Quick Summary
Probability measures how likely an event is to happen. For equally likely outcomes, use P(E) = Favorable Outcomes Γ· Total Possible Outcomes. Probability can be written as a fraction, decimal, or percentage and always falls between 0 and 1.