All Probability Chapter 5 Review 11-25-24

Front

What is the probability of exactly k successes in n trials?

Back

The probability of exactly k successes in n trials can be calculated using the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

Front

What is the mean of a binomial distribution?

Back

The mean (expected value) of a binomial distribution is calculated as: μ = n * p, where n is the number of trials and p is the probability of success.

Front

What is the standard deviation of a binomial distribution?

Back

The standard deviation of a binomial distribution is calculated as: σ = √(n * p * (1 - p)).

Front

How do you calculate combinations?

Back

Combinations are calculated using the formula: C(n, k) = n! / (k! * (n - k)!), where n is the total number of items, and k is the number of items to choose.

Front

What does it mean for two events to be mutually exclusive?

Back

Two events are mutually exclusive if they cannot occur at the same time. For example, rolling a 5 and rolling an even number on a single die.

Front

What is the probability of at least one success in n trials?

Back

The probability of at least one success in n trials is calculated as: P(at least 1) = 1 - P(no successes) = 1 - (1 - p)^n.

Front

What is the law of large numbers?

Back

The law of large numbers states that as the number of trials increases, the sample mean will converge to the expected value.

Front

What is a probability distribution?

Back

A probability distribution describes how the probabilities are distributed over the values of the random variable.

Front

What is the difference between discrete and continuous random variables?

Back

Discrete random variables can take on a countable number of values, while continuous random variables can take on an infinite number of values within a given range.

Front

What is the binomial theorem?

Back

The binomial theorem provides a formula for expanding expressions of the form (a + b)^n, where n is a non-negative integer.