Question

A spinner is divided evenly into 8 sections. There are 4 blue sections, 2 red, 1 green, and 1 yellow. Player A wins if the spinner lands on blue. Otherwise Player B wins. Is the game fair?

Answer 1

To determine if the game is fair, we need to analyze the probabilities of each player winning based on the distribution of sections on the spinner.

The spinner has a total of 8 sections, divided as follows:
- Blue: 4 sections
- Red: 2 sections
- Green: 1 section
- Yellow: 1 section

Player A wins if the spinner lands on blue. Since there are 4 blue sections, the probability that Player A wins is:

\[
P(A \text{ wins}) = \frac{\text{Number of blue sections}}{\text{Total number of sections}} = \frac{4}{8} = \frac{1}{2}
\]

Player B wins if the spinner lands on red, green, or yellow. The total number of sections that lead to Player B's win is:

- Red: 2 sections
- Green: 1 section
- Yellow: 1 section

This totals to:

\[
\text{Total for Player B} = 2 + 1 + 1 = 4 \text{ sections}
\]

The probability that Player B wins is:

\[
P(B \text{ wins}) = \frac{\text{Number of red, green, or yellow sections}}{\text{Total number of sections}} = \frac{4}{8} = \frac{1}{2}
\]

Since both Player A and Player B have an equal probability of winning, which is \(\frac{1}{2}\), we conclude that the game is fair. Thus:

**The game is fair.**