# Role of the Die Statistics

A fair die is rolled until win or loss occurs:

For k=1 to 5: if a 6 occurs on the kth roll you win N dollars and game ends; if a number<k occurs you lose $10 and the game ends; otherwise you roll again.

For k>5: if a 6 occurs on the kth roll you win N dollars and the game ends; if a number<5 occurs you lose $10 and the game ends; if a 5 occurs you roll again.

what value should N have for this game to be fair?

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/statistics/probability/role-of-the-die-statistics-2kg#### Solution Preview

...ou roll again.

what value should N have for this game to be fair?

Solution:

We know that the possibility that 6 occurs for each roll is 1/6. Now if we roll k times where k>5, then the chance of 6 occurs is k/6. Thus the chance of winning N dollars is

(k/6 ...