A binomial distribution is a method that can be used to solve a certain type of problem related to probability. In order to use the binomial distribution, the following must be true about the problem:
- The outcomes are mutually exclusive, that is there are 2 possible outcomes which cannot occur simultaneously (Example: Flipping a coin, there 2 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. (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. (Example: On your second flip of a coin, the first outcome doesn't impact the chances of the next toss. You still have a 50/50 chance of tossing a heads (or tails).)
The binomial distribution is a probability distribution. It has discrete values. It counts the number of successes in yes/no-type experiments. There are two parameters, the number of times an experiment is done (n) and the probability of a success (p). Examples are:
- Tossing a coin 10 times, and counting the number of face-ups. (n=10, p=1/2)
- Rolling a dice 10 times, and counting the number of sixes. (n=10, p=1/6)
- Suppose 5% of a certain population of people have green eyes. 500 people are picked randomly. The number of green-eyed people will follow a binomial distribution (n=500, p=0.05).