Probability Models

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What is a probability model?

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A probability model is a mathematical representation of a random phenomenon, consisting of a sample space and a way to assign probabilities to events.

Tags

CCSS.7.SP.C.7A

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Define expected value in probability.

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The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability.

Tags

CCSS.HSS.MD.A.2

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What is the formula for calculating expected value for a discrete random variable?

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E(X) = Σ [x * P(x)], where x is a value and P(x) is the probability of x.

Tags

CCSS.HSS.MD.A.2

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If 12% of engines have defects, what is the probability that an engine has no defects?

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The probability that an engine has no defects is 1 - 0.12 = 0.88 or 88%.

Tags

CCSS.HSS.CP.B.7

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How do you calculate the expected number of successes in a binomial distribution?

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The expected number of successes is calculated as E(X) = n * p, where n is the number of trials and p is the probability of success.

Tags

CCSS.HSS.MD.A.2

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What is the expected number of correct answers when guessing on a multiple choice test with 4 options?

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If there are n questions, the expected number of correct answers is E(X) = n * (1/4). For 40 questions, E(X) = 40 * 0.25 = 10.

Tags

CCSS.HSS.MD.A.2

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What does it mean for a random variable to follow a binomial distribution?

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A random variable follows a binomial distribution if it counts the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Tags

CCSS.HSS.MD.A.4

CCSS.HSS.MD.A.3

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What is the probability of getting at most k successes in a binomial distribution?

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The probability of getting at most k successes can be calculated using the cumulative distribution function (CDF) of the binomial distribution.

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Define the term 'geometric distribution'.

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A geometric distribution models the number of trials until the first success in a series of independent Bernoulli trials.

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What is the probability of the first success occurring on the nth trial in a geometric distribution?

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The probability is given by P(X=n) = (1-p)^(n-1) * p, where p is the probability of success.