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Dependent Events and Sample Spaces

Probability of an event is affected by the probability of the previous event.

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Independent and Dependent Events

Independent Events

definition: the occurence of one event does not affect the probability of the other event

example: picking a particular card from a deck of cards and rolling a 6 on a die

if A and B are two independent events, then P(A and B) = P(A) * P(B)

Dependent Events

definition: the occurence of one event does affect the probability of the other event

example: taking a red candy out of a bag of candy, eating it, and then taking out another red candy

if A and B are two dependent events, then P(A and B) = P(A) * P(B after A has occured)

Are the following events independent or dependent?

getting an even number on the first roll of a die and getting an even number on the second roll

choosing two cards from a deck with replacement

choosing two cards from a deck without replacement

flipping a coin, and then flipping it again

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