Question

If you roll a standard number cube, determine the probability that you roll an even number or a 5.

Answer 1

To determine the probability of rolling an even number or a 5 on a standard six-sided number cube (or die), we first identify the outcomes.

The outcomes when rolling a die are:
1, 2, 3, 4, 5, 6.

**Step 1: Identify the even numbers and the number 5.**
- The even numbers on the die are: 2, 4, 6.
- The number 5 is one of the outcomes.

**Step 2: List the favorable outcomes.**
- The even numbers (2, 4, 6) make 3 outcomes.
- The number 5 is one additional outcome.

Since 5 is not an even number, we can simply combine these outcomes without overlap:
- Even numbers: 2, 4, 6, 5 → {2, 4, 5, 6}

**Step 3: Count the total favorable outcomes.**
- The total favorable outcomes are: 2, 4, 5, 6, which gives us 4 favorable outcomes.

**Step 4: Calculate the probability.**
- The total possible outcomes when rolling a die is 6.

Thus, the probability \( P \) of rolling an even number or a 5 is given by the formula:

\[
P(\text{even number or 5}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{6} = \frac{2}{3}
\]

Therefore, the probability that you roll an even number or a 5 is \( \frac{2}{3} \).