To find the probability of rolling an odd number or a number less than 4 on a single die, we need to first understand the total possible outcomes and the favorable outcomes for the criteria specified.
A standard die has six faces, numbered from 1 to 6. Let’s break down the two situations:
- Odd Numbers: The odd numbers on a die are 1, 3, and 5. Therefore, the favorable outcomes for rolling an odd number are: 1, 3, 5.
- Numbers Less than 4: The numbers less than 4 are 1, 2, and 3. So, the favorable outcomes for rolling a number less than 4 are: 1, 2, 3.
Next, we can combine these outcomes. Notice that the number 1 and 3 are common in both categories:
- Odd numbers: {1, 3, 5}
- Numbers less than 4: {1, 2, 3}
Now, let’s find the combined favorable outcomes:
- Combined outcomes for either rolling an odd number or a number less than 4: {1, 2, 3, 5}
This results in 4 favorable outcomes: 1, 2, 3, and 5.
Now, let’s calculate the probability:
The probability formula is:
P(A) = (Number of favorable outcomes) / (Total possible outcomes)
In our case:
P(A) = 4 (favorable outcomes) / 6 (total outcomes) = 2/3
Thus, the probability of rolling an odd number or a number less than 4 when rolling a single die is 2/3.