The possible outcomes of a six-sided die are $\{1, 2, 3, 4, 5, 6\}$.

1. Event A: Rolling an even number.

   • The even numbers on a six-sided die are $\{2, 4, 6\}$.
   • So, $P(A) = \frac{3}{6} = \frac{1}{2}$.

2. Event B: Rolling a number less than 4.

   • The numbers less than 4 are $\{1, 2, 3\}$.
   • So, $P(B) = \frac{3}{6} = \frac{1}{2}$.

3. Intersection of A and B: Rolling a number that is both even and less than 4.

   • The only outcome that is both even and less than 4 is $\{2\}$.
   • So, $P(A \cap B) = \frac{1}{6}$.

To find $P(A \cup B)$, we use the formula for the probability of the union of two events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Substituting in the values: $P(A \cup B) = \frac{1}{2} + \frac{1}{2} - \frac{1}{6} = \frac{3}{6} + \frac{3}{6} - \frac{1}{6} = \frac{5}{6}$

Thus, the probability of rolling an even number or a number less than 4 is: $\frac{5}{6}$

Would you like to explore further details on probability calculations or have any questions?

Here are five related questions:

1. What is the probability of rolling an odd number or a number greater than 3?
2. If you roll two dice, what is the probability that both show even numbers?
3. What is the probability of rolling a prime number on a six-sided die?
4. How does the probability change if you roll a die with more than six sides?
5. What is the probability of rolling a 2 or 5 on a six-sided die?

Tip: To calculate the probability of "either/or" events, remember to subtract the intersection if there's overlap between the two events.