Pregunta
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Which of the following are criteria for a binomial probability experiment? Select all that apply. \( \square \) A. There are two mutually exclusive outcomes, success or failure. \( \square \) B. The experiment is performed a fixed number of times. \( \square \) C. The probability of success is the same for each trial of the experiment. \( \square \) D. The probability of success is different for each trial of the experiment. \( \square \) E. There are three mutually exclusive outcomes, arriving on-time, arriving early, and arriving late. \( \square \) F. The experiment is performed until a desired number of successes is reached. \( \square \) G. Each trial depends on the previous trial. \( \square \) H. The trials are independent.

Ask by Hilton Ford. in the United States
Mar 16,2025

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The criteria for a binomial probability experiment are: - A. Two mutually exclusive outcomes (success or failure) - B. Fixed number of trials - C. Constant probability of success for each trial - H. Independence of trials

Solución

**Step 1: Check for Two Possible Outcomes** A binomial experiment should have exactly two outcomes per trial (commonly called success and failure). - \( \boxed{\text{A. There are two mutually exclusive outcomes, success or failure.}} \) This is correct. - \( \boxed{\text{E. There are three mutually exclusive outcomes, arriving on-time, arriving early, and arriving late.}} \) This is incorrect. **Step 2: Fixed Number of Trials** A binomial experiment requires a fixed number of trials. - \( \boxed{\text{B. The experiment is performed a fixed number of times.}} \) This is correct. - \( \boxed{\text{F. The experiment is performed until a desired number of successes is reached.}} \) This describes an experiment with a variable number of trials (negative binomial), so it is incorrect. **Step 3: Constant Probability of Success** Success probability must remain the same throughout all trials. - \( \boxed{\text{C. The probability of success is the same for each trial of the experiment.}} \) This is correct. - \( \boxed{\text{D. The probability of success is different for each trial of the experiment.}} \) This is incorrect. **Step 4: Independence of Trials** Each trial must be independent of the others. - \( \boxed{\text{H. The trials are independent.}} \) This is correct. - \( \boxed{\text{G. Each trial depends on the previous trial.}} \) This is incorrect. **Conclusion:** The criteria for a binomial probability experiment are: \( \boxed{A, B, C, H} \)

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Bonus Knowledge

When it comes to binomial probability experiments, there’s a fun little checklist to keep in mind! Just remember: you need exactly two exclusive outcomes: success or failure (that’s option A). Also, the good ol' law of numbers comes into play—there has to be a fixed number of trials (hello, option B!). And let's not forget: each trial must have the same probability of success (option C) and the trials should be independent, meaning the outcome of one doesn’t affect the others (option H). Now, if you dive just a bit deeper into the world of probability, you’ll encounter delightful applications! Think of a game show where contestants answer questions—every time they get one wrong, it’s like flipping a coin (success or failure) on whether they move on. From predicting weather forecasts to analyzing marketing strategies, binomial experiments are all around us, making numbers and chances as exciting as a rollercoaster ride!

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