Is the game fair or not fair? Explain your answer.
Cooper and Alyssa take turns rolling 3 four-sided dice. If a 1 or 2 is rolled at least once then Cooper gets a point. If a 3 or 4 is rolled at least once, then Alyssa gets a point. (Note that both could get a point on the same roll.
Answer
\(\boxed{\text{The game is fair because both Cooper and Alyssa have the same probability of getting a point in each turn (0.875).}}\)
Step 1 ：Calculate the probability of Cooper getting a point: \(P(C) = 1 - (\frac{1}{2})^3 = \frac{7}{8} = 0.875\)
Step 2 ：Calculate the probability of Alyssa getting a point: \(P(A) = 1 - (\frac{1}{2})^3 = \frac{7}{8} = 0.875\)
Step 3 ：\(\boxed{\text{The game is fair because both Cooper and Alyssa have the same probability of getting a point in each turn (0.875).}}\)
