A die is rolled once. Find the probabilities of the given events. Leave your answer as a reduced fraction.
The number rolled is a 2.   

The number showing is an even number.   

The number showing is greater than 4.   


Let's analyze each event in terms of the probability of a die roll. A standard die has 6 faces, numbered 1 to 6.

1. **The number rolled is a 2:**
   - Only one outcome (rolling a 2) satisfies this event, and there are 6 possible outcomes in total.
   \[
   P(\text{rolling a 2}) = \frac{1}{6}
   \]

2. **The number showing is an even number:**
   - The even numbers on a die are 2, 4, and 6. There are 3 favorable outcomes.
   \[
   P(\text{even number}) = \frac{3}{6} = \frac{1}{2}
   \]

3. **The number showing is greater than 4:**
   - The numbers greater than 4 on a die are 5 and 6. There are 2 favorable outcomes.
   \[
   P(\text{greater than 4}) = \frac{2}{6} = \frac{1}{3}
   \]

So, the probabilities are:
1. \(\frac{1}{6}\) for rolling a 2.
2. \(\frac{1}{2}\) for rolling an even number.
3. \(\frac{1}{3}\) for rolling a number greater than 4.

Would you like more details on any of these steps?

Here are 5 follow-up questions to consider:
1. What is the probability of rolling an odd number?
2. What is the probability of rolling a number less than 3?
3. What is the probability of rolling either a 1 or a 6?
4. If the die is rolled twice, what is the probability of rolling two even numbers?
5. What is the probability of rolling a number that is either less than 3 or greater than 4?

**Tip**: Probabilities for simple events are calculated by dividing favorable outcomes by total possible outcomes.

A die is rolled once. Find the probabilities of the given events. The number rolled is a 2. The number showing is an even number. The number showing is greater than 4.

Discover how to calculate the probability of rolling a 2, an even number, and a number greater than 4 on a die. This problem introduces fundamental probability concepts, including event outcomes and sample space analysis. Ideal for students in Grades 5-7.

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