Question

which of the following is a binomial experiment? rolling a six - sided number cube 24 times and recording if a 4 comes up rolling a six - sided number cube and recording the number until a 4 comes up rolling a six - sided number cube and recording the number until an even number comes up rolling a six - sided number cube 24 times and recording the number that comes up

Explanation:

A binomial experiment has a fixed number of trials, two possible outcomes (success - failure), independent trials, and a constant probability of success. Rolling a six - sided number cube 24 times and recording if a 4 comes up meets these criteria. There are 24 fixed trials, two outcomes (4 comes up or not), trials are independent, and the probability of getting a 4 on each roll is constant ($\frac{1}{6}$). The other options do not have a fixed number of trials (second and third option) or more than two distinct outcomes (fourth option).

Answer:

Rolling a six - sided number cube 24 times and recording if a 4 comes up