Question

you and a friend are playing a game by tossing two coins. if both coins land on heads, you win. if both land on tails, your friend wins. otherwise, nobody wins. the table shows the possible outcomes.

coin 1	coin 2
heads	tails
tails	tails
tails	heads

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.
d. no. you have a \\(\frac{1}{4}\\) probability of winning, while your friend has a \\(\frac{1}{2}\\) probability of winning.

Explanation:

Step1: Count total outcomes

There are 4 possible outcomes (from the table: HH, HT, TT, TH).

Step2: Find your winning outcomes

You win when both are heads (HH), so 1 outcome. Probability: $\frac{1}{4}$.

Step3: Find friend's winning outcomes

Friend wins when both are tails (TT), so 1 outcome. Probability: $\frac{1}{4}$.

Step4: Check fairness

Since both probabilities are $\frac{1}{4}$, the game is fair.

Answer:

A. Yes. You and your friend each have a $\frac{1}{4}$ probability of winning.