Test Review:Geometric vs. Binomial

Front

What is the Binomial Probability Formula?

Back

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

Define 'Geometric Distribution'.

Back

A probability distribution that models the number of trials needed for the first success in a series of independent Bernoulli trials.

Front

What does 'at least' mean in probability?

Back

It refers to the probability of an event occurring a minimum number of times.

Front

What does 'exactly' mean in probability?

Back

It refers to the probability of an event occurring a specific number of times.

Front

How do you calculate the probability of 'at least 2' successes in a binomial distribution?

Back

P(X >= 2) = 1 - P(X < 2) = 1 - (P(X=0) + P(X=1)).

Front

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

Back

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

Front

What is the significance of independent trials in probability?

Back

The outcome of one trial does not affect the outcome of another trial.

Front

What is the probability of not getting a success in a binomial distribution?

Back

It is calculated as (1-p) raised to the power of the number of trials.

Front

How do you find the probability of 'at least 5' successes in a binomial distribution?

Back

P(X >= 5) = 1 - P(X < 5) = 1 - (P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)).

Front

What is the meaning of 'n choose k' in the binomial formula?

Back

It represents the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).