Morgan Stanley Interview Question: There is a big line of people... | Glassdoor

Interview Question

Quantitative Analyst Interview New York, NY

There is a big line of people waiting outside a theatre for

  buying tickets. The theatre owner comes out and announces that the first person to have a birthday same as someone standing before him in the line gets a free ticket. Where wil you stand to maximise your chance?

Interview Answer

6 Answers


Please post some answers guys

Kash on Feb 7, 2011

your are at nth position, the possibility that the people before you have different birthdays is
(365/365)*(364/365)*- - - -*(366-(n-1))

then the possibility that your birthday is in one of these days is

so total probablilty is
(365/365)*(364/365)*- - - -*(366-(n-1))*(n-1/365)
Clearly you should stand where f(n)>f(n-1) and f(n)>f(n+1)


Brett on Apr 5, 2011

Let there are n people before you. The fact that a person's birthday is the same as yours is a Bernoulli trial with probability of success p = 1/366. Probability of exactly 1 success in n trials is f(n) = n*p*(1-p)**(n-1) (1).
To maximize (1), solve df/dn = 0; n = -1 / ln(1-p) ~ 1/p = 366; f(366) = (1-1/366)^365 ~1/e

Anonymous on Nov 4, 2014

First in the line

A. on Oct 26, 2015

Second in line

Anonymous on Aug 23, 2016

Accoring to 2nd post, doing the calculation, I find n = 19?

Anonymous on Oct 14, 2018

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