If a person were to bet on a fair coin toss and on each toss placed a dollar bet on heads with the strategy to quit once ahead by a dollar or after 20 tosses (whichever comes sooner). Assume an infinite bank roll. What is the probability of this person winning $1?
2026-03-26 09:42:40.1774518160
Tossing a fair coin with intention to quit once ahead
74 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
2
HINT: This is the same as the probability that the first passage time of a simple random walk to $S_n =1$ is less than or equal to $20.$ The first passage time $\tau(1)$ has distribution $$P(\tau(1) = 2m-1) = \frac{P(S_{2m-1}=1)}{2m-1}.$$