Binomial and Geometric Probability

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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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What is Geometric Probability?

Back

Geometric Probability is the probability that the first success occurs on the nth trial in a sequence of independent Bernoulli trials.

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What is the formula for Binomial Probability?

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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 is the formula for Geometric Probability?

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P(X=n) = (1-p)^(n-1) * p, where n is the trial on which the first success occurs and p is the probability of success.

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If the probability of success is 0.11, how many trials are expected to get the first success?

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The expected number of trials is 1/p = 1/0.11 ≈ 9.1 trials.

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What does it mean if a variable is Geometric?

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A Geometric variable counts the number of trials until the first success occurs.

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What does it mean if a variable is Binomial?

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A Binomial variable counts the number of successes in a fixed number of trials.

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In a survey, if 38% of people plan to vote for a candidate, how many out of 100 would you expect to vote for them?

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You would expect 38 people to vote for the candidate.

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What is the probability of winning on the third attempt if the chance of winning is 25%?

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The probability of winning on the third attempt is 0.141.

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What is the mean number of beachgoers expected to get sunburned if 32% of them do?

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In a survey of 75 beachgoers, the expected number with sunburn is 0.32 * 75 = 24.