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:

• Independent events are events where the outcome of one event does not affect the outcome of another event.
• Rolling two number cubes: The outcome of one cube roll does not affect the outcome of the other cube roll.
• Choosing a card and then flipping a coin: The result of choosing a card has no impact on the result of flipping a coin.
• Drawing a marble, replacing it and then drawing another: Since the marble is replaced, the first draw does not change the composition of the bag for the second draw.
• Flipping the same coin three times: Each coin flip is an independent event as the previous flip does not influence the next one.
• Choosing first, second, and third - place winners: The choice of the first - place winner affects the pool of candidates for the second and third places (dependent).
• Drawing a name from a hat and keeping it: The first draw changes the number of names in the hat for the second draw (dependent).

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.