Problem 2

Jessie and Sasha come up with the following game. They both randomly generate a 2-digit number, and if the two numbers have a common digit, Jessie wins, if they don't, Sasha wins. They both put a certain amount of money in the pot each round, and the winner of the round takes the money in the pot. If Sasha pays 1 pound per round, how much should Jessie pay to make the game fair? (We assume she can pay an arbitrary amount.) Give your answer as a decimal rounded to 4 decimal points.