To determine the probability of rolling an even number or a 5 on a standard number cube (which has the faces numbered 1 through 6), we first identify the favorable outcomes:
- The even numbers on the cube are 2, 4, and 6. There are 3 even numbers.
- The number 5 is also a specific outcome.
Now, we can list the outcomes:
- Even numbers: 2, 4, 6 (3 outcomes)
- The number 5: 5 (1 outcome)
Since 5 is not an even number, the two events (rolling an even number and rolling a 5) are mutually exclusive. Therefore, we can simply add the number of favorable outcomes:
- Total favorable outcomes = Number of even outcomes + Number of outcomes for 5
- Total favorable outcomes = 3 (even) + 1 (5) = 4
Now we find the total number of possible outcomes on the cube, which is 6 (the numbers 1 through 6).
So, the probability of rolling either an even number or a 5 is given by the ratio of favorable outcomes to the total outcomes:
\[ P(\text{even or 5}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3} \]
Therefore, the probability that you roll an even number or a 5 is \( \frac{2}{3} \).