In the Chapter 12 of the book "Operations Research: An Introduction" written by Hamdy A. Taha, the following question is posed:
You can toss a fair coin up to 7 times. You will win 100 if three tails appear before a head is encountered. What are your chances of winning?
The solution for the problem according to the author is \frac{5}{32}$. Nevertheless, after thinking about the problem and trying a number of possible ways of solving it, I cannot find that specific solution and therefore solve it.
Can anyone one help me to figure out how to solve it?