Sample Question #233 (probability theory – puzzle)

You’re invited to flip a fair coin 100 times. You start with $1. Every time you get heads, you double your money. Every time you get tails, you halve your money.

1) How much would you be willing to pay to enter such a game?

2) What’s the probability of breaking even on your initial investment?

[A real interview question I failed at]

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I was wondering if you tried to calculate your expected final payoff. I think That should be the final answer and it is should be around 8.

Disregard my previous message. I was wrong.

let’s consider a similar but different problem, the other settings are the same.but now the time of tosses is 1000, and you initial cash is enough so thatyou do not need to worry halve the $1. how to answer the same twoquestions as above?thanks.