Question

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.

Explanation:

• For rolling a number cube twice: The outcome of the first roll does not affect the outcome of the second roll.
• For flipping a coin twice: The result of the first flip has no impact on the second flip.
• For drawing a card, replacing it, and then drawing a second card: Since the first - drawn card is replaced, the composition of the deck for the second draw is the same as for the first draw. So the first draw does not influence the second draw.

• When removing a card from a deck and then removing a second card (without replacement), the composition of the deck changes for the second draw. So the two events are dependent.
• When taking a marble out of a bag and then taking a second marble out (without replacement), the number and types of marbles available for the second draw are affected by the first draw. So the two events are dependent.

Answer:

Roll a number cube, and then roll the same number cube again; Flip a coin, and then flip the coin a second time; Draw a card from a deck, replace it, and then draw a second card.