Independent events are such events where the occurrence of any one event does not affect the occurrence of any other event.
<u>Part A:</u> rolling two number cubes at same time does not affect outcome of any one cube. It would be Independent events.
<u>Part B:</u> choosing a card, then flipping a coin according to favourable outcome can affect the result. It would be dependent events.
<u>Part C:</u> choosing a winner, keeping it, then choosing another name depends upon remaining persons. It would be dependent events.
<u>Part D:</u> drawing a marble, replacing it, then drawing another marble does not affect number of marbles in the bag. It would be Independent events.
<u>Part E:</u> 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.