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Interview Question

Quantitative Analyst Interview New York, NY

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?
Answer

Interview Answer

2 Answers

0

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
0

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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