Question

which events are independent? check all that apply.
rolling two number cubes at the same time
choosing a card, and then flipping a coin
choosing a first, second, and third place winner
drawing a name from a hat, keeping it, then drawing another name
drawing a marble from a bag, replacing it, then drawing another marble
flipping the same coin three times

Explanation:

• Rolling two number cubes at the same time: The outcome of one cube doesn't affect the other, so they are independent.
• Choosing a card, and then flipping a coin: The card choice doesn't impact the coin flip, so independent.
• Choosing a first, second, and third place winner: The choice of first affects the remaining for second and third, so dependent.
• Drawing a name from a hat, keeping it, then drawing another name: Removing a name changes the hat's contents, so dependent.
• Drawing a marble from a bag, replacing it, then drawing another marble: Replacing the marble restores the original conditions, so independent.
• Flipping the same coin three times: Each flip is independent of the others.

Answer:

• A. rolling two number cubes at the same time
• B. choosing a card, and then flipping a coin
• E. drawing a marble from a bag, replacing it, then drawing another marble
• F. flipping the same coin three times