Questions / Quant trading, Expected value & odds
A bounded fair walk
Your balance starts at 2 points. Each independent fair coin toss adds or subtracts 1. You stop at balance 0 or 7. What is the probability of stopping at 7? Enter a percentage.
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Answer: 28.57% (2/7)
- Let p be the probability of finishing at 7. The stopped balance is 7 with probability p and 0 otherwise, so 7p = 2 and p = 2/7 = 28.5714%.
Interview shortcut. Fair game, so P(hit top) = start/top = 2/7.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.