Binomial Probability exact

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What is Binomial Probability?

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Binomial Probability is the probability of obtaining exactly k successes in n independent Bernoulli trials, where each trial has two possible outcomes (success or failure) and the probability of success is constant.

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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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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 and is calculated as n! / (k!(n-k)!).

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In a binomial experiment, what are the two outcomes?

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The two outcomes are typically referred to as 'success' and 'failure'.

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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 a success in each trial of the binomial experiment.

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How do you calculate the probability of getting exactly 3 correct answers out of 6 multiple choice questions with 4 options?

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Use the Binomial Probability formula: P(X = 3) = C(6, 3) * (1/4)^3 * (3/4)^(6-3).

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What is the probability of rolling a '4' exactly 15 times in 100 rolls of a fair die?

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Use the Binomial Probability formula with n=100, k=15, and p=1/6.

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How do you find the probability of getting 6 hits in 10 at-bats with a batting average of .298?

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Use the Binomial Probability formula with n=10, k=6, and p=0.298.

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What is the probability of a mower starting exactly 11 times out of 12 pushes if the probability of starting is 0.95?

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Use the Binomial Probability formula with n=12, k=11, and p=0.95.

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How do you calculate the probability of tossing a coin 5 times and getting tails 4 times?

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Use the Binomial Probability formula with n=5, k=4, and p=0.5.