Jane Street Interview Question: 2. In an urn you have red and... | Glassdoor

Interview Question

Quantitative Analyst Interview New York, NY

2. In an urn you have red and blue balls (same number of

balls in each of the two colors). You extract 3 balls what is the probability that the number of balls you have extracted is odd. Now you extract 10 balls, what is the probability that the number of balls you have extracted is odd?

0

what? 3 is an odd number. so the probability you have drawn an odd number of balls after drawing 3 balls is 1

similarly, 10 is an not an odd number. so the the probability you have drawn an odd number of balls after drawing 10 balls is 0

Anonymous on Feb 2, 2011
1

I'm guessing that this question was written incorrectly and it actually should be "odd number of blue balls" or whatever. In which case, the answer, I believe, is always 1/2. For 3, we can work this out

P(odd) = P(exactly 1) + P(exactly 3) = 3C1 * (1/2)^3 + 3C3 * (1/2)^3 = 3/8 + 1/8 = 1/2

working this out for 10 is exactly the same.

P(odd) = P(1) + P(3) + P(5) + P(7) + P(9) = 10C1/1024 + 10C3/1024 + 10C5 / 1024 +10C7/1024 + 10C9 / 1024 = 10/1024 + 120/1024 + 252/1024 + 120/1024 + 10/1024 = 512/1024

Anonymous on Mar 3, 2011
2

it is always one half

Anonymous on Mar 11, 2011
0

For ten balls situation, the sample space is

BBBBBBBBBB
BBBBBBBBBR
BBBBBBBBRR
BBBBBBBRRR
....
BBRRRRRRRR
BRRRRRRRRR
RRRRRRRRRR

There are 11 samples, and 5 of which give you odd number of blue balss. So it is 5/11

Brett on Apr 5, 2011
2

The question is equivalent to (1/2 + 1/2 x)^3, what are the sum of the coefficients at has x^n, where n is odd. Plug x = 1, get 1; plug x = -1; get 0. So sum is (1-0)/2 = 2.
For (1/2+1/2x)^10, it's the same.

JY on Feb 19, 2013
0

For n = 3, answer is 1/2 by symmetry.
For n =10, the original question doesn't assume choose with replacement. If choose with replacement, then it is 1/2. Otherwise, it is slightly smaller than 1/2, depending on the total number of red and blue balls.

Jimmy on Mar 4, 2016