The problem asks to find the probability of rolling either an even number or a number less than 3 on a six-sided die. The sides of the die are numbered 1 through 6.

Step 1: List the outcomes for each condition.

• Even numbers: These are 2, 4, and 6.
• Numbers less than 3: These are 1 and 2.

Step 2: Combine the outcomes.

We need the probability of rolling an even number or a number less than 3. However, we should be careful not to double-count any numbers that meet both conditions. In this case, 2 is both even and less than 3, so we count it only once.

Thus, the distinct outcomes are:

• 1 (less than 3)
• 2 (both even and less than 3)
• 4 (even)
• 6 (even)

So, the favorable outcomes are: 1, 2, 4, 6.

Step 3: Calculate the probability.

There are 4 favorable outcomes (1, 2, 4, 6) out of 6 possible outcomes (since the die has 6 sides).

Thus, the probability is: $P = \frac{4}{6} = \frac{2}{3}$

Final Answer:

The probability is $\frac{2}{3}$.

Would you like more details or have any other questions? Here are some related questions for further exploration:

1. What is the probability of rolling an odd number on a six-sided die?
2. How does the probability change if we use an eight-sided die instead?
3. What is the probability of rolling a number greater than 4 or an even number?
4. Can you calculate the probability of rolling a number that is both even and less than 3?
5. What is the probability of rolling a prime number on a six-sided die?

Tip: When calculating probabilities involving "or" conditions, remember to exclude any overlapping outcomes to avoid double-counting.