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Morgan Stanley Quantitative Analyst Interview Question

I interviewed in New York, NY and was asked:
"A line in front of movie theater, a free ticket is to given to the first person whose birthday is the same as someone who has already bought a ticket. You choose the position in this line, which position have the largest chance of getting the free ticket?"
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Answer

Part of a Quantitative Analyst Interview Review - one of 993 Morgan Stanley Interview Reviews

Answers & Comments

0
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Possibility to win in he nth position:
Pn=(n-1)*364!/365^n/(366-n)!
It is easy to see that Pn/Pn+1 = 1, where n=19.61, so the best place is n=20.
Note that the above calculation uses a 365 day year (no birthday on 29th Febr).

- Andras on Aug 29, 2011
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this is not true for n=2 - if you are second in the line, then probability is 1/365 and formula above gives Pn|n=2 = P[2] = 1/365^2 ...

- Alex on Jun 15, 2012

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