Probability Lecture Review

This set of flashcards covers key concepts from the probability lecture, including fundamental definitions, rules, and important problems.

What is the Monty Hall Problem?

A probability puzzle based on a game show scenario where contestants choose from three doors, one of which has a car behind it.

What happens to your odds if you switch doors in the Monty Hall Problem?

Your odds of winning the car double to 2/3 if you switch doors.

What is Classical Probability?

Probability based on the assumption that outcomes are equally likely.

What is Empirical Probability?

Probability based on the number of times an event occurs relative to the number of trials conducted.

What is Subjective Probability?

Probability based on an individual's personal opinion or available information.

What is the addition rule in probability?

A rule that states if two events are mutually exclusive, the probability of either event occurring is the sum of their individual probabilities.

Define Complement Rule in probability.

The probability of an event not occurring is equal to 1 minus the probability of the event occurring.

What is the Special Rule of Multiplication?

If two events are independent, the probability of both events occurring is the product of their individual probabilities.

Define Gambler’s Fallacy.

The incorrect belief that past independent events affect the probabilities of future independent events.

What is a null hypothesis in statistical testing?

A default assumption that there is no significant difference or relationship between variables.

How is the General Rule of Addition different from the Special Rule of Addition?

The General Rule of Addition is used when events are not mutually exclusive, accounting for the overlap between events.

What does a small P-value (e.g., < 0.05) signify?

A small P-value indicates a very low probability that the null hypothesis is true, suggesting statistical significance.