Question

which of the following is a binomial experiment? flipping a coin until it comes up tails flipping a coin until 8 heads are recorded flipping a coin 10 times and recording if it comes up heads flipping a coin by 10 different people and recording the age of each person

Explanation:

Step1: Recall binomial experiment criteria

A binomial experiment has a fixed number of trials, each trial is independent, there are only two possible outcomes, and the probability of success is constant for each trial.

Step2: Analyze first option

Flipping a coin until it comes up tails has a non - fixed number of trials. So it's not a binomial experiment.

Step3: Analyze second option

Flipping a coin until 8 heads are recorded has a non - fixed number of trials. So it's not a binomial experiment.

Step4: Analyze third option

Flipping a coin 10 times (fixed number of trials), each flip is independent, there are two outcomes (heads or tails), and the probability of getting heads is 0.5 for each flip. This is a binomial experiment.

Step5: Analyze fourth option

Recording the age of people who flip a coin is not related to the two - outcome nature of coin - flipping in a binomial sense. The variable of interest is wrong. So it's not a binomial experiment.

Answer:

Flipping a coin 10 times and recording if it comes up heads