State the criteria for a binomial probability experiment
Choose the correct answer
Each trial has two possible mutually exclusive outcomes success and failure
The experiment consists of a fixed number n of trials
The trials are independent
The probability of success p remains constant for each trial of the experiment?
Yes, all of the above.
Out of the options provided, the correct answer is:
- Each trial has two possible mutually exclusive outcomes: success and failure.
Explanation:
A binomial probability experiment is a situation in which there are a fixed number of trials, each with two possible outcomes (usually labeled as success and failure). For each trial, the outcomes must be mutually exclusive, meaning that only one outcome can occur at a time. Examples of binomial experiments include flipping a coin (where success can be getting heads and failure can be getting tails) or conducting a survey (where success can be someone choosing "yes" and failure can be someone choosing "no").
The other options mentioned are also important in the context of probability experiments, but they do not specifically define the criteria for a binomial probability experiment.
- The experiment consists of a fixed number n of trials: While this is generally true for a binomial experiment, it is not the defining characteristic. The number of trials can vary in other types of probability experiments.
- The trials are independent: Independence means that the outcome of one trial does not affect the outcome of any other trial. This is an important criteria for any probability experiment, including binomial ones, but it is not exclusive to binomial experiments.
- The probability of success p remains constant for each trial of the experiment: Having a constant probability of success for each trial is another important criterion for a binomial experiment, but it is not the only one. The other options mentioned above define the criteria more precisely.
The correct answer is:
- Each trial has two possible mutually exclusive outcomes, success and failure.
- The experiment consists of a fixed number, n, of trials.
- The trials are independent.
- The probability of success, p, remains constant for each trial of the experiment.