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.
Answer
A
Roll a number cube, and then roll the same number cube again.
B
Flip a coin, and then flip the coin a second time.
C
Remove a card from a deck, and then remove a second card.
D
Draw a card from a deck, replace it, and then draw a second card.
E
Take a marble out of a bag, and then take a second marble out of the bag.
Explanation
Two events are independent when the first event does not change the probability of the second. Rolling a number cube again and flipping a coin again do not change the possible outcomes, so A and B are independent. Replacing the card restores the deck before the second draw, so D is independent. Removing a card or marble without putting it back changes what remains, so those draws are dependent.
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