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.
Answer:
1.rolling two number cubes at the same time
2.choosing a card, and then flipping a coin
5.drawing a marble from a bag, replacing it, then drawing another marble
6.flipping the same coin three times
