Question

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

a. 1/12
b. 2/3
c. 1/2
d. 1/6

Answer 1

A standard number cube (or die) has six faces, numbered from 1 to 6. The even numbers on a die are 2, 4, and 6, and there's also the number 5.

We need to find the probability of rolling an even number or a 5.

1. The even numbers on the die are:
- 2
- 4
- 6
This gives us a total of 3 outcomes.

2. There’s also the number 5, which is a single outcome that we have not counted yet.

Now, we combine these outcomes:
- Even numbers: 2, 4, 6 (3 outcomes)
- The number 5 (1 outcome)

However, there is no overlap (we can't roll an even number and a 5 at the same time).

So, the total number of favorable outcomes is:
\[ 3 \text{ (even numbers)} + 1 \text{ (the number 5)} = 4 \text{ favorable outcomes} \]

The total number of possible outcomes when rolling a dice is 6.

Therefore, the probability \( P \) of rolling an even number or a 5 is:
\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{6} = \frac{2}{3}
\]

Thus, the answer is **b. 2/3**.