Binomial Probability

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What is Binomial Probability?

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Binomial Probability refers to the probability of obtaining a fixed number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

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What is the formula for Binomial Probability?

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

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What does 'n' represent in the binomial probability formula?

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In the binomial probability formula, 'n' represents the number of trials.

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What does 'k' represent in the binomial probability formula?

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In the binomial probability formula, 'k' represents the number of successes.

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What does 'p' represent in the binomial probability formula?

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

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What does 'q' represent in the binomial probability formula?

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In the binomial probability formula, 'q' represents the probability of failure on a single trial.

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

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Using the binomial formula, P(X = 5) = (10 choose 5) * (0.5)^5 * (0.5)^5 = 0.2461 or 24.61%.

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What is the probability of getting exactly 3 correct answers when guessing on 6 multiple choice questions with 4 options each?

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The probability is 13.2%.

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How do you calculate 'n choose k'?

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'n choose k' is calculated using the formula n! / (k!(n-k)!), where '!' denotes factorial.

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What is the expected value in a binomial distribution?

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The expected value (mean) is calculated as E(X) = n * p.