Manuals/calci/BINOMIALPROBABILITY

BINOMIALPROBABILTY(NumberOftrials,NumberOfSuccess,ProbabiltyOfSuccess)

• $Numberoftrials$ is the trials occured.
• $NumberofSuccess$ is the success occured.

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)

Examples

1. BINOMIALPROBABILTY(5,3,0.4)=0.23040000000000005
2. BINOMIALPROBABILTY(10,4,0.25)=0.1459980010986328
3. BINOMIALPROBABILTY(12,11,0.75)=0.12670540809631348

See Also

• LEVENESTEST
• MOODSMEDIANTEST
• RIEMANNZETA

References

• Binomial probability