3
AssignmentMultiple Select

Probability of Independent Events

Question 3 • (OC27) MATH COLL LIB ARTS-1207350-S2-Maguire-D'Aquino

Which events are independent? Check all that apply.

Answer
A
rolling two number cubes at the same time
B
choosing a card, and then flipping a coin
C
choosing a first, second, and third place winner
D
drawing a name from a hat, keeping it, then drawing another name
E
drawing a marble from a bag, replacing it, then drawing another marble
F
flipping the same coin three times

Explanation

Events are independent when the outcome of one does not change the probabilities for the next. Rolling two number cubes, choosing a card and flipping a coin, and flipping the same coin three times are independent because each result does not affect the other results. Drawing a marble and replacing it restores the bag to its original contents, so those draws are independent too. Choosing winners without replacement or keeping a name after drawing it changes who is available, so C and D are dependent.

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