Binomial Probability [Exact]

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What is Binomial Probability?

Back

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) * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and nCk is the binomial coefficient.

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

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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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'k' represents the number of successful outcomes we are interested in.

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What does 'p' represent in the Binomial Probability formula?

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'p' represents the probability of success on a single trial.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the binomial coefficient (nCk)?

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The binomial coefficient, denoted as nCk, is calculated as n! / (k!(n-k)!), where '!' denotes factorial, and it represents the number of ways to choose k successes from n trials.

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How do you calculate the probability of at most k successes?

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To calculate the probability of at most k successes, sum the probabilities of getting 0, 1, 2, ..., k successes: P(X ≤ k) = Σ P(X = i) for i = 0 to k.

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What is the probability of getting exactly 10 heads when flipping a coin 20 times?

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Using the binomial formula, the probability is approximately 17.62%.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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If the probability of success is 0.72, what is the probability of making exactly 10 successful free throws out of 11 attempts?

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The probability is approximately 11.53%.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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What is the probability of 2 out of 10 blood donors having Type B blood if the probability of Type B blood is 0.11?

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The probability is approximately 0.214.