Geometric vs. Binomial

Front

What is a geometric distribution?

Back

A geometric distribution models the number of trials until the first success in a series of independent Bernoulli trials, where each trial has the same probability of success.

Front

What is a binomial distribution?

Back

A binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What is the formula for the mean of a geometric distribution?

Back

The mean (expected value) of a geometric distribution is given by E(X) = 1/p, where p is the probability of success.

Front

What is the formula for the standard deviation of a geometric distribution?

Back

The standard deviation of a geometric distribution is given by SD(X) = sqrt((1-p)/p^2).

Front

What is the formula for the mean of a binomial distribution?

Back

The mean (expected value) of a binomial distribution is given by E(X) = n*p, where n is the number of trials and p is the probability of success.

Front

What is the formula for the standard deviation of a binomial distribution?

Back

The standard deviation of a binomial distribution is given by SD(X) = sqrt(n*p*(1-p)).

Front

How do you calculate the probability of exactly k successes in a binomial distribution?

Back

Use the formula 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.

Front

What is the probability of not selling a garment until the 7th customer if 4% buy specialty clothes?

Back

P(X > 6) = (1 - 0.04)^6 = 0.0313.

Front

What is the probability of rolling a 6 for the first time on the 6th roll of a die?

Back

This is not a binomial probability; it is a negative binomial scenario.

Front

If the probability of a red light is 15/50, what is the probability of exactly 3 out of 8 cars stopping at a red light?

Back

Use the binomial formula: P(X = 3) = (8 choose 3) * (15/50)^3 * (35/50)^5 = 0.254.