- Use a binomial distribution to calculate probability
- Determine if a probability model meets the conditions for a binomial distribution
Bernoulli Trial
A Bernoulli trial is a chance experiment with the following three properties:
- There are exactly two possible outcomes of the chance experiment. We label one of them as a success and the other as a failure (these aren’t value judgments on the outcomes, just labels; usually, we call the outcome we’re most interested in the success outcome).
- The probability of success is the same for every trial. We call the probability of success [latex]p[/latex]. Since the only two outcomes are success and failure, the probability of failure is the probability that the trial does not result in a success, so we can use the NOT probability rule to find that the probability of failure is [latex]1-p[/latex].
- The trials are independent from one another. (This means that the outcome of one trial does not affect the likelihood of the possible outcomes of subsequent trials.)
binomial experiment
A binomial experiment is an experiment consisting of a fixed number, [latex]n[/latex], of independent Bernoulli trials that counts the number of successes out of [latex]n[/latex] trials. Notice that the number of successes in a binomial experiment is a discrete random variable.
The distribution of this random variable is modeled with the binomial distribution.