What is the probability of rolling an odd number or a number less than 3 with an unbiased, 6-sided die?

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.

Understand the probability of rolling an odd number or a number less than 3 with a 6-sided die. Detailed step-by-step solution and calculations included. Suitable for Grades 6-8 students and anyone interested in basic probability concepts.

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