4 Gambling [15 points] Suppose a casino has a finite fortune F (e.g., 10.5M$) that is willing to put on a table against you. You play the following game against the casino using a fair coin: if heads (H) appear for the first time after k tosses, the game is over, and you get paid 2* dollars. We agree to toss the coin n times or until it shows up heads, whatever happens first. 1. How much money would you be willing to put on this bet if F=10 500 000$, n = 30? Report your answer with 4 decimal digits of accuracy