This question asks you to distinguish between independent and dependent events.

Part (a): Independent Events

Independent events are those where the occurrence of one event does not affect the occurrence of the other. In this case, Option A: Rolling a die twice is an example of two independent events. The result of the first roll does not influence the result of the second roll.

Part (b): Dependent Events

Dependent events are those where the occurrence of one event affects the probability of the other. Although part (b) is not multiple-choice here, we can look at the options and see which represent dependent events.

Option B (selecting a queen from a deck without replacement and then selecting another queen) is an example of dependent events, because removing one queen affects the probability of drawing a queen on the next draw.

Would you like further details or have any additional questions?

Here are some related questions for further practice:

1. What are mutually exclusive events, and how do they differ from independent events?
2. How do you calculate the probability of two independent events occurring together?
3. Can you give an example of two dependent events involving coins or dice?
4. If two events are mutually exclusive, are they also dependent? Why or why not?
5. How does replacing a card after drawing it affect whether events are independent or dependent?

Tip: When determining if events are independent, think about whether the outcome of one event impacts the likelihood of the other event.