Answer :
To determine which of the scenarios described is a binomial experiment, we need to review the definition and characteristics of a binomial experiment. A binomial experiment must meet the following criteria:
1. The experiment consists of a fixed number of trials.
2. Each trial has exactly two possible outcomes, often termed "success" and "failure."
3. The probability of success is the same for each trial.
4. The trials are independent of each other.
Let's analyze each option based on these criteria:
1. Flipping a coin until it comes up tails:
- This does not have a fixed number of trials. The number of flips depends on when the first tail appears. Therefore, it is not a binomial experiment.
2. Flipping a coin until 8 heads are recorded:
- Similar to the first option, this does not have a fixed number of trials. The number of flips depends on how many flips it takes to get 8 heads. This is not a binomial experiment.
3. Flipping a coin 10 times and recording if it comes up heads:
- This scenario meets all the criteria of a binomial experiment:
- There is a fixed number of trials (10 flips).
- Each trial has two possible outcomes (heads or tails).
- The probability of heads (success) is the same for each flip.
- Each flip is independent of the others.
4. Flipping a coin by 10 different people and recording the age of each person:
- This scenario does not fit the criteria of a binomial experiment because the outcome (the age of each person) is not a binary outcome (success/failure). Additionally, the core element being measured is the age of the person, not the result of the coin flip.
Based on the above analysis, the correct choice that describes a binomial experiment is:
Flipping a coin 10 times and recording if it comes up heads.
1. The experiment consists of a fixed number of trials.
2. Each trial has exactly two possible outcomes, often termed "success" and "failure."
3. The probability of success is the same for each trial.
4. The trials are independent of each other.
Let's analyze each option based on these criteria:
1. Flipping a coin until it comes up tails:
- This does not have a fixed number of trials. The number of flips depends on when the first tail appears. Therefore, it is not a binomial experiment.
2. Flipping a coin until 8 heads are recorded:
- Similar to the first option, this does not have a fixed number of trials. The number of flips depends on how many flips it takes to get 8 heads. This is not a binomial experiment.
3. Flipping a coin 10 times and recording if it comes up heads:
- This scenario meets all the criteria of a binomial experiment:
- There is a fixed number of trials (10 flips).
- Each trial has two possible outcomes (heads or tails).
- The probability of heads (success) is the same for each flip.
- Each flip is independent of the others.
4. Flipping a coin by 10 different people and recording the age of each person:
- This scenario does not fit the criteria of a binomial experiment because the outcome (the age of each person) is not a binary outcome (success/failure). Additionally, the core element being measured is the age of the person, not the result of the coin flip.
Based on the above analysis, the correct choice that describes a binomial experiment is:
Flipping a coin 10 times and recording if it comes up heads.
