Binomial probability refers to an outcome from a binomial experiment, also called a Bernoulli trial. Specifically, the binomial probability tells you the probability of having exactly x successes in a series of trials. You can find a full list of probabilities for binomial experiments in the binomial probability table.
Binomial experiments have the following properties (for more detailed information on what these properties are, read this article on Bernoulli trials).
- The experiment has a certain number of trials, “n”
- The trials must have only two outcomes, a success or failure
- The events must be independent. In other words, the outcome of one trial (like a coin toss) does not affect the outcome of the next trial (like a second coin toss)
- The number of successes in repeated trials of a binomial experiment is called a binomial random variable. For example, if you tossed a coin a hundred times and were counting the number of heads tossed (a “success”) then the binomial random variable should be close to 50.
In order to calculate probabilities for binomial experiments, use the binomial probability formula:
binomial probability formula:
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| Binomial Probability |
The binomial probability formula might look intimidating, but all you’re doing is inserting some key pieces of information into the formula and multiplying:
n = number of trials
k = number of successes
n – k = number of failures
p = probability of success in one trial
q = 1 – p = probability of failure in one trial
How to work a binomial distribution formula.
A binomial probability distribution has a few important properties:
- The variance of a binomial distribution is n*p*(1-P)
- The standard deviation of a binomial distribution is sqrt[n*P*(1-P)]
- The man of a binomial distribution is n*P
