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 nCx⋅px⋅(1−p)n−xnCx⋅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 (1−p)(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⋅(1−16)10−410C4⋅(16)4⋅(1−16)10−4
Simplify.
≈0.054
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