which events are independent? select three options.\n□ roll a number cube, and then roll the same number…

which events are independent? select three options.\n□ roll a number cube, and then roll the same number cube again.\n□ flip a coin, and then flip the coin a second time.\n□ remove a card from a deck, and then remove a second card.\n□ draw a card from a deck, replace it, and then draw a second card.\n□ take a marble out of a bag, and then take a second marble out of the bag.

which events are independent? select three options.\n□ roll a number cube, and then roll the same number cube again.\n□ flip a coin, and then flip the coin a second time.\n□ remove a card from a deck, and then remove a second card.\n□ draw a card from a deck, replace it, and then draw a second card.\n□ take a marble out of a bag, and then take a second marble out of the bag.

Answer

Answer:

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

Explanation:

Step1: Define independent events

Independent events are those where the outcome of one event does not affect the outcome of the other.

Step2: Analyze rolling a number - cube

When rolling a number cube twice, the first roll's result has no impact on the second roll's result.

Step3: Analyze flipping a coin

When flipping a coin twice, the first flip's result (heads or tails) does not influence the second flip's result.

Step4: Analyze drawing cards without replacement

When removing a card from a deck and then removing a second card without replacement, the first - card removal changes the composition of the deck, affecting the second - card draw. So, these are dependent events.

Step5: Analyze drawing cards with replacement

When drawing a card from a deck, replacing it, and then drawing a second card, the deck's composition remains the same for the second draw as it was for the first draw. So, the two draws are independent.

Step6: Analyze taking marbles from a bag

When taking a marble out of a bag and then taking a second marble out of the bag without replacement, the first - marble removal changes the number and types of marbles left in the bag, affecting the second - marble draw. So, these are dependent events.