Binomial Probability exact

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What is Binomial Probability?

Back

Binomial Probability is 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) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does 'n choose k' mean in the context of Binomial Probability?

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'n choose k' (denoted as C(n, k) or nCk) represents the number of ways to choose k successes from n trials.

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If a die is rolled 10 times, what is the probability of never rolling a '4'?

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0.162

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What is the probability of getting exactly 6 heads when tossing a coin 10 times?

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20.51%.

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What is the probability of getting exactly 6 hits in 10 at-bats with a batting average of .298?

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3.58%.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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In a binomial distribution, what does the term 'success' refer to?

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In a binomial distribution, 'success' refers to the outcome of interest, which can vary depending on the context of the problem.

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What is the significance of the probability of success (p) in Binomial Probability?

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The probability of success (p) is crucial as it determines the likelihood of achieving the desired outcome in each trial.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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How do you calculate the probability of getting 5 yellow flowers out of 6 tables if the probability of yellow flowers is 70%?

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The probability is 30.3%.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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What is the relationship between the number of trials and the probability of success in Binomial Probability?

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As the number of trials increases, the distribution of outcomes approaches a normal distribution, given a fixed probability of success.