Which of the following is an example of a binomial experiment?

• A. Flipping a coin $10$ times and counting the number of heads
• B. Measuring the heights of $10$ randomly selected students
• C. Recording the time it takes for $10$ people to run a mile
• D. Rolling a die and recording the sum of the numbers rolled

Answer: (A)

Verified step by step guidance

1. Understand the definition of a binomial experiment: it consists of a fixed number of independent trials, each with only two possible outcomes (commonly called 'success' and 'failure'), and the probability of success remains constant across trials.
2. Analyze each option to see if it meets the criteria of a binomial experiment:
3. For 'Flipping a coin 10 times and counting the number of heads': there are 10 fixed trials, each trial has two outcomes (head or tail), trials are independent, and the probability of heads is constant (usually 0.5). This fits the binomial experiment definition.
4. For 'Measuring the heights of 10 randomly selected students' and 'Recording the time it takes for 10 people to run a mile': these are continuous measurements, not trials with two outcomes, so they are not binomial experiments.
5. For 'Rolling a die and recording the sum of the numbers rolled': the outcome is not binary (there are six possible outcomes per roll), and the sum is a continuous count, so this is not a binomial experiment.