Question

Predicting the Winner
You must roll a total of 9 on two number cubes to win the game. Alex must roll a 6. Who is more likely to win the game on the next turn? Explain.

Answer 1

Assume the two number cubes are fair six-sided dice.

- Total ways to roll two dice = 36.
- Ways to get a sum of 9: (3,6),(4,5),(5,4),(6,3) — 4 outcomes, so P(sum 9) = 4/36 = 1/9 ≈ 11.11%.
- Alex must roll a 6 on one die: P(6) = 1/6 = 6/36 ≈ 16.67%.

Since 1/6 > 1/9 (6/36 > 4/36), Alex is more likely to win on the next turn.