Question

A game includes spinning a spinner with numbers 1–5 and then rolling a number cube with numbers 1–6.What is the probability of getting an even number on both?

Answer 1

To find the probability of getting an even number on both the spinner and the number cube, we first need to identify the even numbers on each.

### Spinner (numbers 1–5):
The even numbers are:
- 2
- 4

**Total even numbers on the spinner**: 2
**Total numbers on the spinner**: 5

**Probability of getting an even number on the spinner**:
\[
P(\text{even on spinner}) = \frac{\text{number of even outcomes}}{\text{total outcomes}} = \frac{2}{5}
\]

### Number Cube (numbers 1–6):
The even numbers are:
- 2
- 4
- 6

**Total even numbers on the number cube**: 3
**Total numbers on the number cube**: 6

**Probability of getting an even number on the number cube**:
\[
P(\text{even on cube}) = \frac{\text{number of even outcomes}}{\text{total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]

### Combined Probability:
To find the probability of both events happening (getting an even number on both the spinner and the number cube), we multiply their individual probabilities:
\[
P(\text{even on both}) = P(\text{even on spinner}) \times P(\text{even on cube}) = \frac{2}{5} \times \frac{1}{2}
\]
\[
P(\text{even on both}) = \frac{2 \times 1}{5 \times 2} = \frac{2}{10} = \frac{1}{5}
\]

Thus, the probability of getting an even number on both the spinner and the number cube is \(\frac{1}{5}\).