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

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.

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

Explanation:

Step1: Define independent events

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

Step2: Analyze each option

  • Rolling a number - cube and then rolling it again: The first roll has no impact on the second roll. The probability of getting a particular number on the second roll is not affected by the result of the first roll.
  • Flipping a coin and then flipping it a second - time: The first coin - flip result does not influence the second coin - flip result. The probability of getting heads or tails on the second flip is the same regardless of the first flip's outcome.
  • Removing a card from a deck and then removing a second card: When the first card is removed, the composition of the deck changes for the second draw. So, these are dependent events.
  • Drawing a card from a deck, replacing it, and then drawing a second card: Since the card is replaced, the deck is in its original state for the second draw. The first draw does not affect the second draw.
  • Taking a marble out of a bag and then taking a second marble out of the bag: When the first marble is taken out, the number and types of marbles in the bag change for the second draw. So, these are dependent events.

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.