Question

algebra i b-cr
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:

Independent events are those where the outcome of the first event does not affect the probability of the second event.

1. Rolling a number cube twice: The result of the first roll doesn't change the possible outcomes or probabilities of the second roll.
2. Flipping a coin twice: The result of the first flip has no impact on the second flip's probability.
3. Drawing a card, replacing it, then drawing again: Replacing the card restores the deck to its original state, so the first draw doesn't affect the second.

The other options involve without replacement, which changes the probability of the second event, making them dependent.

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