Probability Puzzle Time!
Writing about web page http://www.gchq.gov.uk/recruitment/careers/math_apply.html
This puzzle from the GCHQ recruitment website has completely flummouxed me. I suspect there is some sort of general method to dealing with stuff like this, but I have no idea what it is.
2. Alice and Bob play coin toss: Alice pays Bob £1 for each head and Bob pays Alice £1 for each tail they throw. They continue playing until one player loses (runs out of money). Initially Alice has £6 and Bob has £14.
a. Determine, with proof, the probability that Alice loses.
b. Determine the probability that Alice loses but also has at some time previously been within £1 of winning.