# Binomial distribution facts for kids

In probability and statistics, the **binomial distribution** is a probability distribution which models the probabilities of having a certain number of successes among *n* identical trials (each having *p* as the probability of success). It is also written as . The variables n and p are thus the two parameters of a binomial distribution.

The binomial distribution has discrete values. It counts the number of successes in yes/no-type experiments. Each of these experiment, also called Bernoulli trial, either results in success or failure. Examples of binomial distribution include:

- Tossing a coin 10 times, and counting the number of
*face-up*s. (n=10, p=1/2) - Rolling a dice 10 times, and counting the number of sixes. (n=10, p=1/6)
- Counting the number of green-eyed people among 500 randomly chosen people (assuming that 5% of all people have green eyes). (n=500, p=0.05)

In order to use the binomial distribution, the following must be true about the problem:

- The outcomes are
**mutually exclusive**, that is, there are two possible outcomes which cannot occur simultaneously (for example. in flipping a coin, there are two possible outcomes:**heads**or**tails**. It is always one or the other, never both or a mix of outcomes). - The probability of a success (p) is consistent throughout the problem (for example, a basketball player makes 85% of his free throws. Each time the player attempts a free throw, 85% is assumed to be the likelihood of a made shot).
- The trials are
**independent**of each other (for example, on the second flip of a coin, the first outcome does not impact the chance of the next toss: the chance of tossing a heads (or tails) is still 50%).

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Binomial distribution Facts for Kids. *Kiddle Encyclopedia.*