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The binomial distribution density function provides the probability that X success will occur in N trials of a binomial experiment.

A binomial experiment has the following properties.

One common example of a binomial experiment is a sequence of N tosses of a coin.


To find the binomial distribution function of X successes in N trials, denoted f(X), we let p denote the probability of success on any one trial. Then the probability of failure on any one trial is q=1-p. Then the probability of any particular sequence of X success (heads) out of N trials (tosses) is p^X*q^(N-X). But, there are a variety of sequences of tosses that will result in X successes out of N trials. Then, using the formula for the number of ways of obtaining X successes out of N trials, we find that the number of ways of picking X objects out of N objects that there are

Then the probability of N successes out of N trials is given by the FunctioN?:

       F(X)=  (N) *  p^X*q^(N-X) = (N) * p^X*(1-p)^(N-X)                                    
              (X)                  (X)

For example, consider the experiment of tossing a die with the usual 6 sides. Suppose we want to know the probability of getting three "1"s in 5 tosses. Then p=1/5. So q=4/5.

Then, using the function of the binomial distribution function for 3 successes out of 5 trials we get the probability of this occurring as:

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Last edited February 18, 2001 3:10 am by RoseParks (diff)