Question

you and a friend are playing a game by tossing two coins. if both coins land on heads, you win. if the coins land on different sides, your friend wins. the table shows the possible outcomes. is this a fair game? a. yes. you and your friend each have a \\( \frac { 1 } { 4 } \\) probability of winning. b. yes. you and your friend each have a \\( \frac { 1 } { 2 } \\) probability of winning. c. no. you have a \\( \frac { 1 } { 2 } \\) probability of winning, while your friend has a \\( \frac { 1 } { 4 } \\) probability of winning.

Explanation:

Step1: Count total outcomes

Total possible outcomes = 4 (HH, HT, TT, TH)

Step2: Calculate your winning probability

Your win: HH (1 outcome). Probability = $\frac{1}{4}$

Step3: Calculate friend's winning probability

Friend's win: HT, TH (2 outcomes). Probability = $\frac{2}{4} = \frac{1}{2}$

Step4: Compare probabilities

Your probability ($\frac{1}{4}$) ≠ Friend's probability ($\frac{1}{2}$), so not fair.

Answer:

C. No. You have a $\frac{1}{4}$ probability of winning, while your friend has a $\frac{1}{2}$ probability of winning.