Question 2 • Fall 24 GMS Geometry: Concepts and Connections B
Which events are independent? Check all that apply.rolling two number cubes at the same timechoosing a card, and then flipping a coinchoosing a first, second, and third place winnerdrawing a name from a hat, keeping it, then drawing another name drawing a marble from a bag, replacing it, then drawing another marbleflipping the same coin three times
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 all involve separate outcomes that do not affect one another. Drawing a marble, replacing it, and drawing again also keeps the probabilities the same. Choosing winners or keeping a drawn name out of the hat changes who remains available, so those events are dependent.
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