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

Independent events are such events where the occurrence of any one event does not affect the occurrence of any other event.

Part A: rolling two number cubes at same time does not affect outcome of any one cube. It would be Independent events.

Part B: choosing a card, then flipping a coin according to favourable outcome can affect the result. It would be dependent events.

Part C: choosing a winner, keeping it, then choosing another name depends upon remaining persons. It would be dependent events.

Part D: drawing a marble, replacing it, then drawing another marble does not affect number of marbles in the bag. It would be Independent events.

Part E: flipping any coin three times does not affect past or future outcomes. It would be Independent events.

Hence, options A, D, and E are Independent events.

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