Question

Which of the following sets of events are considered independent events?

I. A coin is flipped and a die is rolled.

II. A card is drawn from a deck and replaced, then a second card is drawn.

III. A card is drawn from a deck, not replaced, then a second card is drawn.

Question 3 options:

I only


I and III only


I and II only


II only


III only

Answer 1

To determine which sets of events are considered independent, we can analyze each option:

I. A coin is flipped and a die is rolled.
- The outcome of flipping a coin does not affect the outcome of rolling a die. Therefore, these two events are independent.

II. A card is drawn from a deck and replaced, then a second card is drawn.
- Since the first card is replaced, the outcome of the first draw does not affect the second draw, making these two events independent.

III. A card is drawn from a deck, not replaced, then a second card is drawn.
- In this case, the outcome of the first draw affects the probabilities of the second draw (the deck now has one fewer card and potentially affects the composition of the remaining cards). Therefore, these two events are dependent.

Based on this analysis, events I and II are independent.

So, the correct answer is:

**I and II only**.