Manuals/calci/BINOMIALPROBABILITY

BINOMIALPROBABILTY(NumberOftrials,NumberOfSuccess,ProbabiltyOfSuccess)

Description

This function gives the probability value of the Binomial distribution.
A binomial experiment has the following characteristics:
1.The experiment involves repeated trials.
2.Each trial has only two possible outcomes - a success or a failure.
3.The probability that a particular outcome will occur on any given trial is constant.
4.All of the trials in the experiment are independent.
A binomial probability refers to the probability of getting EXACTLY r successes in a specific number of trials.
The number of trials refers to the number of attempts in a binomial experiment.
The number of trials is equal to the number of successes plus the number of failures.
When computing a binomial probability, it is necessary to calculate and multiply three separate factors:
1. the number of ways to select exactly r successes,
2. the probability of success (p) raised to the r power,
3. the probability of failure (q) raised to the (n - r) power.
The formula for Binomial probability is:

${\binom {n}{r}}p^{r}.q^{n-r}$ or : ${\binom {n}{r}}p^{r}(1-p)^{n-r}$

where n = number of trials,r = number of specific events you wish to obtain.
p = probability that the event will occur, q = probability that the event will not occur.(q = 1 - p, the complement of the event)