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.