Questions: In a binomial exporiement, what does it mean to say thet 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.

In a binomial exporiement, what does it mean to say thet 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.
Transcript text: In a binomial exporiement, what does it mean to say thet 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.
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Solution

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Solution Steps

Solution Approach

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 the option that reflects this definition.

Step 1: Understanding Independence in Probability

In probability theory, two events are considered independent if the occurrence of one event does not affect the probability of the occurrence of the other event. This concept is crucial in a binomial experiment, where each trial is independent of the others.

Step 2: Analyzing the Options

We are given four options to determine which one correctly defines independence in the context of a binomial experiment:

  • Option 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.
  • Option B: Each trial is independent of the other trials if no more than one trial occurs at a time.
  • Option C: Each trial is independent of the other trials if the outcome of one trial affects the outcome of another trial.
  • Option D: Each trial is independent of the other trials if the sum of all the possible trial outcomes equals 1.
Step 3: Selecting the Correct Definition

The correct definition of independence in a binomial experiment is that the outcome of one trial does not affect the outcome of any other trial. This is precisely what Option A states.

Final Answer

The correct answer is \(\boxed{\text{A}}\).

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