Questions: In a binomial experiement, what does it mean to say that each trial is independent of the other trials? Choose the correct answer below. A. Each trial is independent of the other trials if the outcome of one trial does not affect the outcome of any of the other trials. B. Each trial is independent of the other trials if no more than one trial occurs at a time. C. Each trial is independent of the other trials if the outcome of one trial affects the outcome of another trial. D. Each trial is independent of the other trials if the sum of all the possible trial outcomes equals 1 .

Solution Steps

The question is asking for the definition of independence in the context of a binomial experiment. In probability theory, trials are considered independent if the outcome of one trial does not affect the outcome of any other trial. Therefore, the correct answer is option A.

In a binomial experiment, trials are defined as independent if the outcome of one trial does not influence the outcome of any other trial. This means that the probability of success or failure in one trial remains constant regardless of the results of previous trials.

We evaluate the provided options:

• A: Each trial is independent of the other trials if the outcome of one trial does not affect the outcome of any of the other trials. (This is true.)
• B: Each trial is independent of the other trials if no more than one trial occurs at a time. (This is false.)
• C: Each trial is independent of the other trials if the outcome of one trial affects the outcome of another trial. (This is false.)
• D: Each trial is independent of the other trials if the sum of all the possible trial outcomes equals 1. (This is false.)

Based on the analysis, the correct definition of independence in trials is option A.

Final Answer