Alice and Finn roll two number cubes. Which of the following rules will make the game fair?
Alice wins if a total of 5 is rolled. Finn wins if a total of 9 is rolled.
Alice wins if a total of 7 is rolled. Finn wins if a total of 8 is rolled.
Alice wins if a total of 3 is rolled. Finn wins if a total of 10 is rolled.
Alice wins if a total of 4 is rolled. Finn wins if a total of 11 is rolled.
Would it be the second one?
To determine which rule will make the game fair, we need to consider the probability of each outcome.
When rolling two number cubes, there are 36 possible outcomes (6 possible outcomes for Alice's roll multiplied by 6 possible outcomes for Finn's roll).
1. For the first rule, Alice wins if a total of 5 is rolled. There are four possible outcomes that result in a total of 5: (1,4), (2,3), (3,2), and (4,1). Therefore, the probability of Alice winning is 4/36 (or simplified as 1/9). Finn wins if a total of 9 is rolled, and there are two possible outcomes that result in a total of 9: (3,6) and (4,5). The probability of Finn winning is 2/36 (or simplified as 1/18).
2. For the second rule, Alice wins if a total of 7 is rolled. There are six possible outcomes that result in a total of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The probability of Alice winning is 6/36 (or simplified as 1/6). Finn wins if a total of 8 is rolled, and there are five possible outcomes that result in a total of 8: (2,6), (3,5), (4,4), (5,3), and (6,2). The probability of Finn winning is 5/36.
3. For the third rule, Alice wins if a total of 3 is rolled. There is only one possible outcome that results in a total of 3: (1,2). The probability of Alice winning is 1/36. Finn wins if a total of 10 is rolled, and there are three possible outcomes that result in a total of 10: (4,6), (5,5), and (6,4). The probability of Finn winning is 3/36 (simplified as 1/12).
4. For the fourth rule, Alice wins if a total of 4 is rolled. There are three possible outcomes that result in a total of 4: (1,3), (2,2), and (3,1). The probability of Alice winning is 3/36 (or simplified as 1/12). Finn wins if a total of 11 is rolled, and there is only one possible outcome that results in a total of 11: (5,6). The probability of Finn winning is 1/36.
Out of these options, the second rule is indeed the fairest because both Alice and Finn have equal probabilities of winning (1/6 for both of them).