Each trial has only two possible outcomes — success or failure.
The probability of success p is the same in every trial. The probability of failure q is 1-p.
The random variable X is the number of successes in n trials.
Let's now consider the given experiment to determine whether it is a binomial experiment or can be reduced to a binomial experiment.
A poll found that 65 % of high school teachers own a pet. You ask 15 high school teachers if they own a pet.
Recall that 65 %, written as a decimal, is 0.65. Therefore, when we ask if a teacher has a pet, we can think of the responses as having the following probabilities.
ccc
Response & Variable & Probability
Yes & p & 0.65
No & 1- p = q & 1- 0.65= 0.35
Let's see if the experiment satisfies the conditions.
Condition
Explanation
Is it Satisfied?
1.
Each trial is asking the question to a singular teacher. There is a fixed number of independent trials, n=15.
✓
2.
Success is yes, failure is no.
✓
3.
The probability of success is the same in every trial, p=0.65. The probability of failure is q=0.35.
✓
4.
The random variable X is the number of yes responses.
✓
Since the experiment satisfies the conditions, it is a binomial experiment.
