Hey guys,
I'm interviewing for some special sits funds, and they told me some MDs like to ask some probability brainteasers to the candidates.
I'm trying to have a look at the most classical brainteasers, but would love to make a list of questions you have been asked during your interviews. this could be a good thread where we could put together the most asked/difficult brainteasers.
Thanks1
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How would you size a position that you could lose 100% if you're wrong but earn 150% if you're right?
What is the chance that two people in a room of 75 have their birthdays on the same day? See https://en.wikipedia.org/wiki/Birthday_problem
What would the solution to your first question be? You can't use Kelly formula as you don't know the actual probabilities of winning.
I would suggest setting probability of winning as p therefore EV = 1.5(p)+(-1)(1-p) = 2.5p -1 (not sure how to use this info though). Now I would size the initial bet as 1/3 of total as (1-100/150 =1/3). and then do this a few times to get a value for the actual probability of a win and use the kelly formula
Is this right? Please explain where I've gone wrong if not,
Isn't 100% loss as 0? I.e you go broke? so actually in a way a 100% drawdown is game over, and that;s why it takes a lot of more time to reach breakeven from big drawdowns vs any gains you may have?
thanks a lot - very helpful!
In an interview setting, are you expected to calculate the actual probabilities for the second question?
Or is the series p = 1 - (364/365)(363/365)... (365-75/365) enough?
Ask your candidate to find out how much salt it would take to cover all the roads of his native city to prevent freezing
The answer to the 2nd question about the birthdays is: P = 1-(364/365)^(75C2) = 1- (364/365)^2625 ~ 0.99925... or >99.9%.
Are you sure you are expected to give a numerical answer to this question?
Assuming you will not have calculator with you during the interview.
Is it enough to tell your interviewer that the odds are more than 99.9%?
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