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.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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.

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CCSS.HSS.MD.A.2

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.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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.

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CCSS.HSS.MD.A.2

Front

What is the formula for the probability of an event?

Back

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

Tags

CCSS.7.SP.C.7A

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.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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.

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CCSS.HSS.CP.A.1

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.

Tags

CCSS.7.SP.C.7A