A.P. Statistics Chapter 6B: Binomial and Geometric Prob. 24-25

Front

What is a binomial probability?

Back

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

Front

Define the parameters of a binomial distribution.

Back

The parameters of a binomial distribution are n (the number of trials) and p (the probability of success on each trial).

Front

What is the formula for calculating binomial probabilities?

Back

The formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where k is the number of successes.

Front

What is a geometric probability?

Back

A geometric probability is the probability that the first success occurs on the k-th trial in a series of independent Bernoulli trials.

Front

Define the parameters of a geometric distribution.

Back

The parameter of a geometric distribution is p (the probability of success on each trial).

Front

What is the formula for calculating geometric probabilities?

Back

The formula is P(X = k) = (1-p)^(k-1) * p, where k is the trial on which the first success occurs.

Front

What does it mean for trials to be independent in a binomial setting?

Back

It means that the outcome of one trial does not affect the outcome of another trial.

Front

What is the significance of a fixed number of trials in a binomial setting?

Back

It ensures that the number of attempts is predetermined, allowing for the calculation of probabilities based on that fixed number.

Front

What is the probability of getting exactly k successes in n trials if p = 0.5?

Back

Use the binomial formula: P(X = k) = (n choose k) * (0.5)^k * (0.5)^(n-k).

Front

How do you calculate the probability of getting more than a certain number of successes in a binomial distribution?

Back

You can calculate it by finding the cumulative probability for that number and subtracting it from 1.