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AP Statistics1. Chapter 8 Reviewable:Binomial vs Geometric: (a) How are the Binomial and Geometric distributions the same? Outcomes are Success / Fail Outcomes are independent Probability of success,
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To fill out a binomial distribution, you need to know the number of trials (n), the probability of success (p), and the number of desired successes (x). Once you have these values, you can use the binomial probability formula to calculate the probability of getting exactly x successes in n trials.
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To fill out a geometric distribution, you need to know the probability of success (p) and the number of trials until the first success occurs (x). Once you have these values, you can use the geometric probability formula to calculate the probability of getting the first success on the x-th trial.

Who needs binomial vs geometric?

01
Binomial distributions are useful when you have a fixed number of independent trials with two possible outcomes (success or failure), and you want to calculate the probability of obtaining a specific number of successes.
02
Geometric distributions are useful when you have a sequence of independent trials with two possible outcomes (success or failure), and you want to calculate the probability of the first success occurring on a specific trial.
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Binomial and geometric distributions are two different types of probability distributions in statistics. The binomial distribution is used when there are only two possible outcomes (success or failure) for each trial, while the geometric distribution is used when the probability of success remains constant for each trial.
Anyone conducting statistical analysis or research that involves outcome probabilities or counting the number of trials may need to use the binomial or geometric distribution.
To fill out a binomial distribution, you need to know the number of trials, the probability of success, and the number of successes you are interested in. To fill out a geometric distribution, you need to know the probability of success for each trial.
The purpose of using binomial and geometric distributions is to model and analyze situations where there are a fixed number of trials with a certain probability of success for each trial.
The information that must be reported includes the number of trials, the probability of success, and the number of successes in the case of a binomial distribution. For a geometric distribution, the probability of success for each trial must be reported.
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