You and a friend are playing a game by tossing two coins . If both coins are heads or both are tails, you win. Otherwise , your friend wins. The table show the possible outcomes. Coin 1 Coln 2 Heads Heads Heads Tails Tails Tails Tails Heads Is this a fair game? A. Yes. You and your friend each have a (1)/(4) probability of winning. B. Yes. You and your friend each have a (1)/(2) probability of winning. C. No. You have a (1)/(2) probability of winning , while your friend has a (1)/(4) probability of winning. D. No. You have a (1)/(4) probability of winning ,while your friend has a (1)/(2) probability of winning.

To determine if the game is fair, we need to calculate the probability of you winning and the probability of your friend winning.First, let's find the total number of possible outcomes when tossing two coins. Each coin has 2 possible outcomes (Heads or Tails), so the total number of outcomes for two coins is:\[2 \times 2 = 4\]Now, let's identify the outcomes where you win. You win if both coins show Heads or both coins show Tails. From the table provided, we can see that there are two outcomes that satisfy this condition:1. Heads & Heads2. Tails & TailsSo, there are 2 favorable outcomes for you to win out of 4 possible outcomes. The probability of you winning is:\[\frac{\text{Number of favorable outcomes for you}}{\text{Total number of possible outcomes}} = \frac{2}{4} = \frac{1}{2}\]Next, let's identify the outcomes where your friend wins. Your friend wins if one coin shows Heads and the other shows Tails. From the table, there are two outcomes that satisfy this condition:1. Heads & Tails2. Tails & HeadsSo, there are 2 favorable outcomes for your friend to win out of 4 possible outcomes. The probability of your friend winning is:\[\frac{\text{Number of favorable outcomes for your friend}}{\text{Total number of possible outcomes}} = \frac{2}{4} = \frac{1}{2}\]Since both you and your friend have the same probability of winning (\(\frac{1}{2}\)), the game is fair.**The accurate answer is B. Yes. You and your friend each have a \(\frac{1}{2}\) probability of winning.**