Binomial distributions
When there are many independent trials (also called experiments or samples) and each trial has two exact outcomes, a Bernoulli distribution is generalized to the binomial distribution. The binomial distribution measures the number of successes in a sequence of independent experiments, each asking a yes/no question.
The real-world examples
The following two examples explain the binomial distribution well:
- What is the probability of finding students who passed the final exam when examining 50 students? Suppose the probability of students passing the exam is 0.8. This can be described by a binomial distribution, p(50,0.8).
- What is the probability of finding drivers who do not have car insurance when examining 100 drivers? Suppose the probability/proportion of drivers not having car insurance is 0.05. This can be described by a binomial distribution as p(100,0.05).
All these examples have the following common elements:
- A fixed number...
