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 probability of getting at least 2 successes in a binomial distribution with n=10 and p=0.11?

Back

0.303

Front

How do you calculate the expected number of trials until the first success in a geometric distribution?

Back

The expected number of trials is calculated as E(X) = 1/p, where p is the probability of success.

Front

What is the expected number of blood donors to collect one with Type B blood if the probability is 0.11?

Back

9.1 donors.

Front

What is a continuous random variable?

Back

A continuous random variable can take any value within a given range, such as the time it takes to complete an exam.

Front

What is a discrete random variable?

Back

A discrete random variable can take only specific values, such as the number of correct answers on a quiz.

Front

What is the formula for the probability of exactly k successes in a binomial distribution?

Back

P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials and p is the probability of success.

Front

What does it mean for trials to be independent in probability?

Back

Independent trials mean that the outcome of one trial does not affect the outcome of another trial.

Front

How do you find the cumulative probability for a binomial distribution?

Back

You sum the probabilities of getting k or fewer successes, P(X ≤ k).