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. Independent.
• Choosing a card, then flipping a coin: Card choice doesn't affect coin flip. Independent.
• Choosing first, second, third place: Choosing first affects remaining for second/third. Dependent.
• Drawing a name, keeping it, then another: Removing a name changes the pool. Dependent.
• Drawing a marble, replacing it, then another: Replacing keeps the pool same. Independent.
• Flipping the same coin three times: Each flip is independent of others. Independent.

Answer:

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