Question

Which of the following situations qualify as a binomial experiment? Explain your answers.

1) An experiment in which a basketball player who historically makes 80% of his free throws is asked to shoot three free throws, and the number of free throws made is recorded.

2) Tossing a coin 20 times to see how many tails occur.

3) A probability experiment in which three cards are drawn from a deck without replacement and the number of aces is recorded.

4) Rolling a die until a 6 appears.

5) Asking 20 people how old they are and record the results.

Answer 1

1)This situation qualifies as a binomial experiment because There are a fixed number of trials (three free throws) and each
trial has two possible outcomes: either the basketball player makes the free throw or misses it.
2) This situation also qualifies as a binomial experiment because there are a fixed number of trials (20 coin tosses).
3) This situation does not qualify as a binomial experiment because it violates the criterion of independent trials.
4) This situation does not qualify as a binomial experiment because it does not have a fixed number of trials. The number of trials can vary depending on how many times the die is rolled until a 6 appears.
5) This situation does not quality as a binomial experiment because it does not have two possible outcomes for each trial. The age of each person can vary, so the outcomes are not binary (either yes or no, success or failure).

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