you roll a six sided die, what is the probability of rolling an even number or less than 4? Answer as a reduced fraction in the form a/b

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.

Learn how to calculate the probability of rolling an even number or a number less than 4 on a six-sided die. This problem explores key probability concepts such as the union of events and intersection of events, using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Suitable for students in Grades 6-8.

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