# Don't roll a six!

**Discrete Mathematics**Level 3

Matthew plays a game with a die (shaped like a cube, has six numbers, {1,2,3,4,5,6} on it). First, he pays a fee of 10€ to start the game. Then he rolls the die. If he rolls a 6, the game ends. In other cases, he wins 1€ and rolls again. If he can avoid the 6 now, he wins 2€ and goes on, otherwise he wins nothing and the game ends.

Matthew goes on rolling the die until he rolls a 6, and every time he rolls a number other than 6, he wins 1€ more than on the previous roll. What is the probability for Matthew's total earnings to be more than 250€? Give the answer as the value of *a* with the accuracy of two decimals, when the probability is *a*%, .