Binomial Experiments

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What is a binomial experiment?

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A binomial experiment is a statistical experiment that has the following properties: 1) It consists of n identical trials. 2) Each trial has two possible outcomes: success or failure. 3) The probability of success, denoted by p, is the same for each trial. 4) The trials are independent.

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What is the binomial probability formula?

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The binomial probability formula is given by 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 does 'n choose k' mean in the context of binomial experiments?

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'n choose k', denoted as C(n, k) or nCk, represents the number of ways to choose k successes in n trials and is calculated as n! / (k!(n-k)!).

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What is the difference between binompdf and binomcdf?

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binompdf(n, p, k) calculates the probability of getting exactly k successes in n trials, while binomcdf(n, p, k) calculates the cumulative probability of getting at most k successes in n trials.

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If a coin is flipped 10 times, what is the probability of getting exactly 5 heads?

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Use the formula: P(X = 5) = (10 choose 5) * (0.5)^5 * (0.5)^(10-5) = 0.2461.

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What is the probability of getting at most 3 heads when flipping a fair coin 5 times?

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Use binomcdf(5, 0.5, 3) to find the cumulative probability of getting 0, 1, 2, or 3 heads.

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In a binomial experiment, what does the variable 'p' represent?

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In a binomial experiment, 'p' represents the probability of success on a single trial.

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What is the expected value of a binomial distribution?

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The expected value (mean) of a binomial distribution is calculated as E(X) = n * p, where n is the number of trials and p is the probability of success.

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What is the variance of a binomial distribution?

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The variance of a binomial distribution is calculated as Var(X) = n * p * (1 - p).

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If the probability of rain on any given day is 0.3, what is the probability of it raining exactly 2 days in a week?

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Use binompdf(7, 0.3, 2) to calculate the probability.