Which of the following scenarios describes a binomial experiment?

• A. A factory tests $20$ light bulbs and records whether each bulb is defective or not.
• B. A company records the time it takes for each of $10$ employees to complete a task.
• C. A researcher measures the exact heights of $50$ randomly selected plants.
• D. A student rolls a die repeatedly until a six appears and counts the number of rolls needed.

Answer: (A)

Verified step by step guidance

1. Recall 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. Examine each scenario to check if it meets the criteria of a binomial experiment:
3. For the first scenario: testing 20 light bulbs and recording whether each bulb is defective or not. Here, there are 20 fixed trials, each bulb can be defective (success) or not defective (failure), and the trials are independent with a constant probability of defectiveness. This fits the binomial experiment definition.
4. For the second scenario: recording the time it takes for each of 10 employees to complete a task. The outcome is a continuous measurement (time), not a binary outcome, so this is not a binomial experiment.
5. For the third scenario: measuring the exact heights of 50 plants. This is also a continuous measurement, not binary, so it is not binomial.
6. For the fourth scenario: rolling a die repeatedly until a six appears and counting the number of rolls. This is a geometric experiment because the number of trials is not fixed in advance; it depends on when the first success occurs, so it is not binomial.