Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
Rolling two 1s followed by one 2 on three tosses of a fair die.
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Part 1
Choose the correct answer below.
​(Type an integer or a simplified​ fraction.)

To determine if these events are independent or dependent, let's analyze them:

### Independence
Two events are independent if the outcome of one event does not affect the outcome of the other. Rolling a die is a classic example of an independent event because each roll is separate and does not influence the outcome of the others. Therefore, each roll in this scenario is independent.

### Combined Probability
For independent events, the probability of combined events happening in a specific sequence is the product of the individual probabilities of each event.

1. **Probability of rolling a 1 on the first roll**: Since a die has 6 faces, the probability of rolling a 1 is:
   \[
   P(\text{1 on first roll}) = \frac{1}{6}
   \]

2. **Probability of rolling

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event. Rolling two 1s followed by one 2 on three tosses of a fair die.

Learn how to determine whether events are independent or dependent and calculate the probability of rolling two 1s followed by a 2 on three tosses of a fair die. This problem covers concepts in probability, independent events, and uses the multiplication rule. Suitable for students in Grades 9-10.

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