Binomial and Geometric Review

Front

What is the probability of the first success occurring on the 10th trial in a geometric distribution?

Back

Use the formula: P(X=k) = (1-p)^(k-1) * p, where p is the probability of success.

Front

What is the formula for finding the probability of getting exactly k successes in n trials in a binomial distribution?

Back

Use the formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

Front

What does it mean when we say each observation falls into one of two categories: 'success' or 'failure'?

Back

This indicates a binomial or geometric distribution, where outcomes are binary.

Front

What is the probability of rolling doubles when rolling two dice?

Back

The probability is 1/6.

Front

If a person has a 0.09 probability of having a certain gene, what is the probability that the first person tested is the 10th person with the gene?

Back

Use the geometric probability formula: geometpdf(0.09, 10).

Front

What is the probability of getting doubles exactly twice in four rolls of a die?

Back

Use the binomial probability formula with n=4, k=2, and p=1/6.

Front

What is the expected value of a binomial distribution?

Back

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

Front

What is the variance of a binomial distribution?

Back

The variance is Var(X) = n * p * (1-p).

Front

What is the cumulative distribution function (CDF) for a geometric distribution?

Back

The CDF gives the probability that the first success occurs on or before the k-th trial.

Front

What is the difference between a binomial and a geometric distribution?

Back

A binomial distribution counts the number of successes in a fixed number of trials, while a geometric distribution counts the number of trials until the first success.