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A mathematical function that provides a model for the probability of each value of a discrete random variable occurring.
For a discrete random variable that has a finite number of possible values, the function is sometimes displayed as a table, listing the values of the random variable and their corresponding probabilities.
A probability function has two important properties:
1. For each value of the random variable, values of a probability function are never negative, nor greater than 1.
2. The sum of the values of a probability function, taken over all of the values of the random variable, is 1.
Example 1
Let X be a random variable with a binomial distribution with n = 6 and π = 0.4. The probability function for random variable X is:
Probability of x successes in 6 trials, P(X = x) = 
for x = 0, 1, 2, 3, 4, 5, 6
where 
is the number of combinations of n objects taken x at a time.
A graph of this probability function is shown below.
Example 2
Imagine a probability activity in which a fair die is rolled and the number facing upwards is recorded. Let random variable X represent the result of any roll.
The probability function for random variable X can be written as:
| x | 1 | 2 | 3 | 4 | 5 | 6 |
| P(X = x) | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 |
Alternative: probability model
See: model
Curriculum achievement objectives reference
Probability: (Level 8)
