Question

two friends, andrew and liz, are playing a game using this spinner. if the spinner lands on region 2, andrew wins. if it lands on region 1, liz wins. if it lands on any other region, neither wins. is this a fair game? a. no. andrew has a \\( \frac { 1 } { 8 } \\) probability of winning and liz has a \\( \frac { 1 } { 4 } \\) probability of winning. b. no. andrew has a \\( \frac { 1 } { 4 } \\) probability of winning and liz has a \\( \frac { 1 } { 8 } \\) probability of winning. c. yes. each friend has a \\( \frac { 1 } { 4 } \\) probability of winning. d. yes. each friend has a \\( \frac { 1 } { 8 } \\) probability of winning.

Explanation:

Step1: Count spinner regions

The spinner has 8 equal regions (labeled 1-5, with regions 2 and another likely split; visual shows region 2 is 1/8, region 1 is 1/4).

Step2: Calculate winning probabilities

Andrew wins on region 2: $P(\text{Andrew}) = \frac{1}{8}$. Liz wins on region 1: $P(\text{Liz}) = \frac{1}{4}$.

Step3: Check fairness

A fair game requires equal winning probabilities. $\frac{1}{8}
eq \frac{1}{4}$, so not fair.

Answer:

A. No. Andrew has a $\frac{1}{8}$ probability of winning and Liz has a $\frac{1}{4}$ probability of winning.