Probability distributions, Expected Value and Fair Games

Front

What is a probability distribution?

Back

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

Front

What is the expected value in probability?

Back

The expected value is the long-term average value of a random variable, calculated as the sum of all possible values, each multiplied by its probability.

Front

What is a discrete random variable?

Back

A discrete random variable is a variable that can take on a countable number of distinct values.

Front

What is a continuous random variable?

Back

A continuous random variable is a variable that can take on an infinite number of values within a given range.

Front

How do you calculate the expected value of a discrete random variable?

Back

Multiply each possible value by its probability and sum all the results.

Front

What is the formula for the probability of an event?

Back

P(Event) = Number of favorable outcomes / Total number of outcomes.

Front

What does it mean for a game to be fair?

Back

A game is considered fair if all players have an equal chance of winning, meaning the expected value of the game is zero.

Front

What is the complement of an event?

Back

The complement of an event is the set of all outcomes in which the event does not occur.

Front

How do you find the probability of at least one event occurring?

Back

P(at least one) = 1 - P(none).

Front

What is the sum of probabilities in a probability distribution?

Back

The sum of all probabilities in a probability distribution must equal 1.