To find the probability of rolling an odd number or a number less than 4, we first identify the total outcomes possible when rolling a single die. A standard die has 6 faces, numbered 1 through 6. Thus, the total outcomes are:
- 1
- 2
- 3
- 4
- 5
- 6
Next, we need to identify the favorable outcomes for our conditions:
- The odd numbers on a die are: 1, 3, and 5.
- The numbers less than 4 on a die are: 1, 2, and 3.
Now, let’s combine both conditions:
- Odd numbers: 1, 3, 5
- Numbers less than 4: 1, 2, 3
The union of these two sets (the odd numbers and numbers less than 4) is: 1, 2, 3, 5. We count the favorable outcomes:
- 1 (odd, and less than 4)
- 2 (not odd)
- 3 (odd, and less than 4)
- 5 (odd)
Thus, the favorable outcomes are 1, 2, 3, and 5, making a total of 4 favorable outcomes. Now we can calculate the probability:
Probability = (Number of Favorable Outcomes) / (Total Number of Outcomes) = 4 / 6 = 2 / 3.
Hence, the probability of rolling an odd number or a number less than 4 is 2/3.