Binomial Probability

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What is the Binomial Probability Formula?

Back

P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n = number of trials, k = number of successes, p = probability of success, q = probability of failure.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

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

Back

The number of trials.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

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

Back

The number of successes.

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What is a Binomial Distribution?

Back

A probability distribution that summarizes the likelihood that a value will take on one of two independent outcomes under a given set of parameters.

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What are the assumptions of a Binomial Distribution?

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1. Fixed number of trials (n). 2. Each trial is independent. 3. Each trial has only two outcomes (success or failure). 4. The probability of success (p) is constant.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

If a coin is tossed 10 times, what is the probability of getting exactly 6 heads?

Back

20.51%.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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

Back

17.62%.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

Front

How do you calculate the probability of getting exactly 'k' successes in 'n' trials?

Back

Use the binomial probability formula: P(X = k) = (nCk) * (p^k) * (q^(n-k)).

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the value of 'p' in a fair coin toss?

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0.5 (the probability of getting heads).

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CCSS.7.SP.C.5

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What is the value of 'q' in a fair coin toss?

Back

0.5 (the probability of getting tails).

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CCSS.7.SP.C.5