Question

april and sanjay are both using tools to simulate the probability that a family with three children will have exactly one girl. april is using a coin, with tails up representing a boy and heads up representing a girl. she flipped the coin three times. sanjay rolled a number cube three times with odd numbers representing a boy and even numbers representing a girl. which statement best describes their simulations? both simulations have the same theoretical probability of a 3 - child family having exactly one girl, but their experimental probabilities may differ. the simulations have different theoretical probabilities of a 3 - child family having exactly one girl, and the experimental probabilities they generate may differ. the simulations have different theoretical probabilities of a 3 - child family having exactly one girl, but their experimental probabilities will be the same. both simulations have the same theoretical probability of a 3 - child family having exactly one girl, and their experimental probabilities will be the same.

Explanation:

In April's coin - flipping simulation, the probability of getting heads (girl) or tails (boy) in each flip is 0.5. In Sanjay's number - cube rolling simulation, the probability of getting an even number (girl) or an odd number (boy) is also 0.5. The theoretical probability of having exactly one girl in a 3 - child family is calculated using binomial probability. For both simulations, the underlying probability model for each trial is the same (50 - 50 chance of boy/girl), so the theoretical probabilities are the same. However, experimental probabilities are based on actual trials and can vary from one set of trials to another.

Answer:

Both simulations have the same theoretical probability of a 3 - child family having exactly one girl, but their experimental probabilities may differ.