5. Lucky Sevens
Setup
Two players, Fizz and Grumb, take turns.
On each turn, a player rolls two fair six-sided dice.
Rules
The first player to roll a sum of exactly 7 wins immediately.
Fizz goes first.
Question
What is the probability that Fizz wins?
Answer format
Enter a number rounded to 2 decimal places or fraction a/b.
Your Answer
Need help?
Hint 1
What is the probability of rolling a 7 with two dice?
Hint 2
If Fizz doesn't win on turn 1, and Grumb doesn't win on turn 2, the game resets to the same state.
Hint 3
Set up an equation: P(Fizz wins) = P(wins turn 1) + P(both miss) × P(Fizz wins)