Question

Which of the following describes independent events?

a.) benny randomly selects what chores to do from his chore list. he selects making his bed first, and crosses the chore off his list. next, he chooses to vacuum the room.
b.) beanie randomly chooses a queen from a standard deck of cards. she sets the card aside and chooses again. this time, she chooses an ace.
c.) bailey randomly picks colored marbles from a bag. she first selects a red marble from the bag, and gives it to a friend. she then selects a green marble from the bag.
d.) ben randomly flips a standard two-sided coin. the first time he flips it, he gets heads. the second time he flips it, he gets tails.

Answer 1

In the given scenarios, flipping a coin twice represents independent events while picking items from a list or cards from a deck without replacement represents dependent events. The correct answer is option b.

Step-by-step explanation:

Independent events in probability refer to events where the outcome of one event does not affect the outcome of another event. When considering whether or not events are independent, a standard skill in high school mathematics, we often look at examples such as coin flips or card draws. Let's address the given scenarios.

Are the Events Independent?

For the student's questions, the scenario of Ben randomly flipping a standard two-sided coin twice (option d) describes independent events because the outcome of the first flip (heads) does not affect the outcome of the second flip (tails). Each coin flip is independent and has no bearing on the other flips

On the other hand, selecting items or cards without replacement (options a, b, and c) are examples of dependent events because removing an item changes the probability of subsequent selections. However, if a card is selected and then placed back into the deck before the next selection (sampling with replacement), the events would be independent, as the deck remains unchanged after each selection.