# Binomial Probability Help

Binomial probability refers to the probability of exactly xx successes on nn repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment).

If the probability of success on an individual trial is pp , then the binomial probability is nCxpx(1p)nxnCx⋅px⋅(1−p)n−x .

Here nCxnCx indicates the number of different combinations of xx objects selected from a set of nn objects. Some textbooks use the notation(nx)(nx) instead of nCxnCx .

Note that if pp is the probability of success of a single trial, then (1p)(1−p) is the probability of failure of a single trial.

If the outcomes of the experiment are more than two, but can be broken into two probabilities pp and qq such that p+q=1p+q=1 , the probability of an event can be expressed as binomial probability.

For example, if a six-sided die is rolled 1010 times, the binomial probability formula gives the probability of rolling a three on 44 trials and others on the remaining trials.

The experiment has six outcomes. But the probability of rolling a 33 on a single trial is 1616 and rolling other than 33 is 5656 . Here, 16+56=116+56=1 .

The binomial probability is:

10C4(16)4(116)10410C4⋅(16)4⋅(1−16)10−4

Simplify.

0.054

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