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) = (nCk) * (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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The number of trials.

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

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The number of successes.

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

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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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The probability of failure on a single trial, where q = 1 - p.

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If a quarterback has a passing percentage of 70%, what is the probability he does NOT complete 8 of his 20 passes?

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11.44%.

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If you flip a coin 20 times, what is the probability of getting at least 13 heads?

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13.16%.

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What is the probability of getting at least 1 correct answer when guessing on 5 multiple choice questions with 4 choices each?

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0.7627.

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What is a Bernoulli trial?

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A Bernoulli trial is a random experiment where there are only two possible outcomes: success or failure.