Let's go over the probabilities for each event related to rolling a die.

(a) Probability that the number showing is a 5:

A standard die has 6 faces numbered 1 through 6. The probability of rolling a 5 is simply the chance of landing on that specific number. Since there is only 1 face with a 5, the probability is:

$P(\text{rolling a 5}) = \frac{1}{6}$

(b) Probability that the number showing is an even number:

The even numbers on a standard die are 2, 4, and 6. So, there are 3 possible outcomes that are even. The probability is:

$P(\text{even number}) = \frac{3}{6} = \frac{1}{2}$

(c) Probability that the number showing is greater than 2:

The numbers greater than 2 on a standard die are 3, 4, 5, and 6. So, there are 4 possible outcomes. The probability is:

$P(\text{number greater than 2}) = \frac{4}{6} = \frac{2}{3}$

Would you like more details or clarifications on any of these solutions?

Here are five related questions to deepen your understanding:

1. What is the probability of rolling a number less than 4?
2. What is the probability of rolling a prime number on a die?
3. If a die is rolled twice, what is the probability of getting two even numbers?
4. What is the probability of rolling a number that is a multiple of 3?
5. How does the probability change if you use a die with more or fewer faces?

Tip:

Always ensure you know the total number of possible outcomes when calculating probabilities, as it serves as the denominator in your fraction.