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:

Independent events are those where the outcome of one event does not affect the outcome of the other. Rolling a number - cube twice, flipping a coin twice, and drawing a card with replacement are independent because the first action does not change the probabilities for the second action. Removing a card without replacement or taking marbles out of a bag without replacement change the probabilities for the second action, so they are 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