To determine whether the given experiment is a binomial experiment, we need to check if it meets the following criteria:
1. The experiment consists of a fixed number of identical trials: In this case, the researcher is observing the gender of the next 100 babies born at a local hospital. Since this number is fixed, the first criterion is met.
2. Each trial has two possible outcomes: The possible outcomes in this case are boy or girl, making it a binary choice. Therefore, the second criterion is met.
3. The probability of success (p) is the same for each trial: The question states that boys and girls are equally likely, meaning the probability of a boy or a girl is 0.5 or 50%. Therefore, the third criterion is met.
4. The trials are independent: Each baby's gender does not affect the gender of the next baby. Therefore, the fourth criterion is met.
Having confirmed that all four criteria are satisfied, we can conclude that the given experiment is a binomial experiment.