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A family of theoretical distributions that is useful as a model for some discrete random variables. Each distribution in this family gives the probability of obtaining a specified number of successes in a specified number of trials, under the following conditions:
• The number of trials, n, is fixed
• The trials are independent of each other
• Each trial has two outcomes; ‘success’ and ‘failure’
• The probability of success in a trial, π, is the same in each trial.
Each member of this family of distributions is uniquely identified by specifying n and π. As such, n and π, are the parameters of the binomial distribution and the distribution is sometimes written as binomial(n , π).
Let random variable X represent the number of successes in n trials that satisfy the conditions stated above. The probability of x successes in n trials is calculated by:
P(X = x) = 
for x = 0, 1, 2, ..., n
where .jpg)
is the number of combinations of n objects taken x at a time.
Example
A graph of the probability function for the binomial distribution with n = 6 and π = 0.4 is shown below.
Curriculum achievement objectives reference
Probability: Level 8
