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
The correct answer is: Each trial has two possible mutually exclusive outcomes (success and failure), and the probability of success remains constant for each trial of the experiment.
To determine the criteria for a binomial probability experiment, we need to consider the following conditions:
1. Two Possible Outcomes: Each trial in the experiment should have two possible outcomes, usually referred to as success and failure. These outcomes must be mutually exclusive, meaning that only one of them can occur on each trial.
2. Fixed Number of Trials: The experiment should consist of a fixed number of trials, denoted by the variable "n". This means that there is a predetermined number of times the experiment will be repeated.
3. Independence: The trials should be independent of each other, meaning that the outcome of one trial does not affect the outcomes of subsequent trials. Each trial should be unrelated and unaffected by the previous or future trials.
4. Constant Probability of Success: The probability of success, denoted by the variable "p", should remain constant for each trial of the experiment. This means that the probability of achieving success should stay the same throughout all the trials.
In summary, a binomial probability experiment must have two possible outcomes (success and failure) that are mutually exclusive, consists of a fixed number of trials, has independent trials, and maintains a constant probability of success.