Section 6.2 The Binomial Probability Distribution
ΒΆDefinition 6.2.1.
A binomial probability distribution is a discrete probability distribution that describes probabilities for experiments in which there are two mutually exclusive outcomes.
An experiment is said to be a binomial experiment if:
The experiment is performed a fixed number of times. Each repetition of the experiment is called a trial.
The trials are independent. This means that the outcome of one trial will not affect the outcome of the other trials.
For each trial, there are two mutually exclusive outcomes success or failure.
The probability of success is the same for each trial.
Reading Questions Reading Questions
Determine whether or not the following probability experiments are binomial experiments.
1.
An experimental drug is administered to 100 randomly selected individuals, with the number of individuals responding favorably recorded.
This is a binomial experiment.
2.
Surveying customers entering a sporting goods store until a customer responds that he or she is shopping for a bicycle.
This is not binomial because the number of trials (surveys of customers) is not fixed.
3.
Record the number of songs downloaded in a month for a group of 30 randomly selected college students.
Not binomial, because the value being recorded (number of songs downloaded) could take on many more values than just two (success or failure).
4.
Observing that ten out of the next twenty customers at a grocery store checkout use a credit card given that the probability of using a credit card is 0.58.
This is a binomial experiment.