Binomial Vs Geometric Distributions

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What is a Binomial Distribution?

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A Binomial Distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

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What is a Geometric Distribution?

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A Geometric Distribution models the number of trials needed to achieve the first success in a series of independent Bernoulli trials.

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When is a Binomial Distribution used?

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It is used when there are a fixed number of trials, each with two possible outcomes (success or failure), and the probability of success is constant.

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When is a Geometric Distribution used?

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It is used when we are interested in the number of trials until the first success occurs, with each trial being independent.

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What is the formula for the Binomial Probability?

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P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

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What is the formula for the Geometric Probability?

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P(X = k) = (1-p)^(k-1) * p, where k is the trial on which the first success occurs and p is the probability of success.

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Example of a Binomial Distribution scenario.

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Flipping a coin 10 times and counting the number of heads.

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Example of a Geometric Distribution scenario.

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Finding the first defective item in a series of quality checks.

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What does 'n' represent in Binomial Distribution?

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'n' represents the number of trials or experiments conducted.

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What does 'p' represent in both distributions?

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'p' represents the probability of success on each trial.