To find the probability of rolling an even number or a 5 on a standard number cube (which has faces numbered from 1 to 6), we will first identify the outcomes.
The even numbers on a standard number cube are: 2, 4, and 6. So, the outcomes for even numbers are: {2, 4, 6}.
The outcome for rolling a 5 is: {5}.
Now, we need to find the combined outcomes for rolling an even number OR a 5. We combine the outcomes: {2, 4, 6, 5}.
In total, we have the following numbers that satisfy the condition:
- Even numbers: 2, 4, 6 (3 outcomes)
- Plus 5 (1 outcome)
So the favorable outcomes are {2, 4, 5, 6}, which gives us a total of 4 successful outcomes.
The total number of possible outcomes when rolling a die is 6 (1, 2, 3, 4, 5, 6).
Now we can find the probability: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{6} = \frac{2}{3} \]
So the answer is \( \frac{2}{3} \).