Binomial Probability Help
Binomial probability refers to the probability of exactlysuccesses on 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, then the binomial probability is .
Hereindicates the number of different combinations of objects selected from a set of objects. Some textbooks use the notation instead of .
Note that ifis the probability of success of a single trial, then 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 probabilitiesand such that , the probability of an event can be expressed as binomial probability.
For example, if a six-sided die is rolledtimes, the binomial probability formula gives the probability of rolling a three on trials and others on the remaining trials.
The experiment has six outcomes. But the probability of rolling aon a single trial is and rolling other than is . Here, .
The binomial probability is: