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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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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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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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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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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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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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' stand for in the binomial probability formula?

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Probability of Successes.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does 'q' stand for in the binomial probability formula?

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Probability of Failures.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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

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The probability is approximately 24.61%.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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What is the probability of getting at least one success in a binomial experiment?

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P(at least 1 success) = 1 - P(0 successes).

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In a binomial distribution, what is the mean (expected value)?

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The mean is calculated as μ = n * p.

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CCSS.HSS.MD.A.2

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In a binomial distribution, what is the variance?

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The variance is calculated as σ² = n * p * q.