To find the probability of rolling an odd number or a number less than 3 with an unbiased 6-sided die, we need to consider the possible outcomes.

Step 1: Identify the outcomes.

• The set of possible outcomes for a 6-sided die is: $\{1, 2, 3, 4, 5, 6\}$.

Step 2: Define the events.

• Event A: Rolling an odd number. The odd numbers on a 6-sided die are $\{1, 3, 5\}$.
• Event B: Rolling a number less than 3. The numbers less than 3 are $\{1, 2\}$.

Step 3: Find the union of the events.

• The union of events A and B (odd numbers or numbers less than 3) is the set of outcomes $\{1, 2, 3, 5\}$.

Step 4: Calculate the probability.

• There are 4 favorable outcomes $\{1, 2, 3, 5\}$ and 6 possible outcomes in total.
• The probability is given by: $P(\text{A or B}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{6} = \frac{2}{3}$

Conclusion:

The probability of rolling an odd number or a number less than 3 is $\frac{2}{3}$.

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

1. What is the probability of rolling a prime number on a 6-sided die?
2. What is the probability of rolling an even number or a number greater than 4?
3. What is the probability of rolling a number that is both odd and less than 4?
4. What is the probability of rolling a multiple of 3 on a 6-sided die?
5. How does the probability change if you use a 10-sided die instead?

Tip: When calculating probabilities involving "or" events, make sure to consider if the events overlap to avoid double-counting any outcomes.