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

To determine which of the given scenarios is a binomial experiment, we need to recall the characteristics of a binomial experiment. A binomial experiment must satisfy the following conditions: 1. There are a fixed number of trials (n). 2. Each trial has only two possible outcomes (success or failure). 3. The trials are independent. 4. The probability of success (p) is the same for each trial. Now, let's analyze each option: 1. **Rolling a six-sided number cube 24 times and recording if a 4 comes up**: - Fixed number of trials: 24 - Two outcomes: "4 comes up" (success) or "4 does not come up" (failure) - Trials are independent. - Probability of success (rolling a 4) is the same for each trial. - **This is a binomial experiment.** 2. **Rolling a six-sided number cube and recording the number until a 4 comes up**: - Not a fixed number of trials; it continues until a 4 is rolled. - This is a geometric experiment, not a binomial experiment. 3. **Rolling a six-sided number cube and recording the number until an even number comes up**: - Similar to the previous option, it is not a fixed number of trials. - This is also a geometric experiment, not a binomial experiment. 4. **Rolling a six-sided number cube 24 times and recording the number that comes up**: - This does not have just two outcomes; it records the specific number rolled (1, 2, 3, 4, 5, or 6). - This is not a binomial experiment. Based on this analysis, the only option that qualifies as a binomial experiment is: **Rolling a six-sided number cube 24 times and recording if a 4 comes up.**