Which events are independent? Select three options. Roll a number cube, and then roll the same number cube again. Flip a coin, and then flip the coin a second time. Remove a card from a deck, and then remove a second card. Draw a card from a deck, replace it, and then draw a second card. Take a marble out of a bag, and then take a second marble out of the bag.

Independent events mean that the result of the first one does not affect the second.

A) Roll a number cube, and then roll the same number cube again.

The result of the first roll does not affect the result of the second roll, so these events are independent.

B) Flip a coin, and then flip the coin a second time.

Same as before, the result of the first flip does not affect the possibilities for the second flip, so these events are independent.

C) Remove a card from a deck, and then remove a second card.

Suppose that the first card that you remove is the 4 of hearts, in the second event you can not remove the 4 of hearts (because you already removed it) so the result of the first event has an effect on the second event, those events are not independent.

D) Draw a card from a deck, replace it, and then draw a second card.

In this case you replace the card, so you can draw the same card again, this means that in this case the events are independent.

E) Take a marble out of a bag, and then take a second marble out of the bag.

After you take a marble of the bag, the total number of marbles in the bag is smaller, so for the second event you will have a marble less than in the first event, and depending on what marble you take in the first event the probabilities for the second event may change, so these events are not independent.