Question

question 4 of 10
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.

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

Explanation:

Step1: Calculate the probability of you winning

There are 4 possible outcomes. You win when both coins are heads (1 outcome). So the probability of you winning is $\frac{1}{4}$.

Step2: Calculate the probability of your friend winning

Your friend wins when coins land on different sides. There are 2 such outcomes (Heads - Tails and Tails - Heads). So the probability of your friend winning is $\frac{2}{4}=\frac{1}{2}$.

Answer:

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