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: The first, second, and fourth.

Step-by-step explanation:

1). When you roll a cube twice, the number you get on the first roll doesn’t impact the second. As a result, it’s independent.

2). When you flip a coin twice, what you get on the first flip doesn’t impact what you get on the second. As a result, it’s independent.

3). When you remove a card from a deck, then remove a second one WITHOUT replacing the first, the first card impacts the second draw. For example, when I draw the first card, my chances of drawing a two are 1/13. If I draw a two the first time, my chances of drawing a two the second time are 1/17 (3/51. The total is fifty-one since one card is missing). Since the first draw impacted the probability of the second, the events are NOT independent.

4). When you remove a card, replace it, then draw again, your chances of drawing the same card doesn’t change. For example, my odds of drawing a three are 1/13 (or 4/52). If I draw a three the first time, then put it back and draw again, my odds are still 1/13 because I put the card back in the deck. As a result, the event is independent.

5). If I take a marble from a bag, and then take a second marble, the first draw impacts the second. For example, if a bag has three blue marbles and three green marbles, my chances of getting a blue marble the first time are 1/2 (or 3/6). If I get a blue marble and choose again, WITHOUT replacing it, my chances of choosing another blue marble are 2/5 (since one marble is missing). Since the first draw impacting the probability of the second, the events are NOT independent.

Answer: A, B , D

Step-by-step explanation:

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