Events are considered to INDEPENDENT EVENTS be independent if: Events E and F are independent events if P(FE) = P(F) or P(E|F) = P(E). PRODUCT RULE...
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Conditional probability may need to be considered

with independent/dependent events. For example: You draw a card from a deck and, without replacing it, you draw a second card.

1 st draw: 2nd draw:


You flip a coin. You flip the coin again.

1 st flip: 2nd flip: 

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Are the following events independent?

Drawing a card from a deck, without replacing it, drawing another card.


Drawing a card from a deck, replacing it, drawing another card.


Flipping a coin twice.


Flipping a coin. Rolling a die.


Choosing a name off the course roster to be the president. Choosing another name to be the vice president.

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Events are considered to
INDEPENDENT EVENTS
be independent if:
Events E and F are independent events if
P(FE) = P(F)
or
P(E|F) = P(E).
PRODUCT RULE FOR INDEPENDENT EVENTS
Events E and F are independent events if and only if
P(EnF) = P(E) . P(F).

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