## Interview Question

Trader Assistant Intern Interview Chicago, IL

# What is the chance that at least two people were born on

the same day of the week if there are 3 people in the room?

0

~89.8%

Anonymous on Nov 22, 2010
0

incorrect.

1-364/365*363/365 = 1-.9918 = .0082...something like this for 2 people, for 2+ add in the chance of 3 of 3.

So first guy then gets 365/365 choices, next two get 1/365

Chase Schwalbach on Jan 18, 2011
5

Also incorrect...

They are asking if they were born the same day of the week not the exact same day as Chase alluded to.

In this case the easiest way to do the problem is 1- probability that no one was born on the same day.

1-(1)(6/7)(5/7)+ 19/49 or 38.78%

2

trader guy on Jan 22, 2011
4

Or you can calculate it directly:
The chance of SELECTED two people(but not three) that are born on the same day is 1* 1/7 - 1/7*1/7 =6/49 Now we have 3 chooses 2 = 3 possible pairs, so the probability that any PAIR(but not all three) that are born on the same day is 3* 6/49 = 18/49. However, since the question asks "at least 2", we will need to add the possibility that all three are born at the same day, which is 1/7 * 1/7 = 1/49.
So the final result is 18/49 + 1/49 = 19/49
This obviously is a worse way of calculating it, but it's an alternative for some people who wants to think "straight".

K Z on Mar 26, 2011