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 72 % of the students plan on going to the homecoming dance. You ask 30 students if they are going to the dance.
Recall that 72 %, written as a decimal, is 0.72. Therefore, when a student is asked if they will go to the dance, we can think of the responses as having the following probabilities.
ccc
Response & Variable & Probability
Yes & p & 0.72
No & 1- p = q & 1- 0.72= 0.28
Let's see if the experiment satisfies the conditions.
Condition
Explanation
Is it Satisfied?
1.
Each trial is asking the question to a singular student. There is a fixed number of independent trials, n=30.
✓
2.
Success is yes, failure is no.
✓
3.
The probability of success is the same in every trial, p=0.72. The probability of failure is q=0.28.
✓
4.
The random variable X is the number of yes responses.
✓
Since the experiment satisfies the conditions, it is a binomial experiment.
