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Liquid Capital Options Trader Interview Question

I interviewed in London, England (UK) and was asked:
"If there was a drawer in front of me containing 4 socks, either black or white, and I know that I have a 50% probability of pulling out two white socks in a row, then what is the probability of pulling out two black socks?"
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Answer

Part of a Options Trader Interview Review - one of 5 Liquid Capital Interview Reviews

Answers & Comments

1
of 4
votes

There is zero probability of pulling two black socks.

- Interview Candidate on Jul 21, 2010
0
of 1
vote

Assuming there are 2 whites and 2 blacks then getting 2 socks of the same colour is the same

- Anonymous on Aug 23, 2012
0
of 0
votes

Above meant to say: Has the same probability

- Anonymous on Aug 23, 2012
0
of 0
votes

You can't assume there are two white socks and two black socks. This problem is an easy enumeration problem actually.
From the problem, you have at least 2 white socks, otherwise it would be impossible to take out 2 in a row. So you have either 2 white socks, 3 or 4.

Just compute the three prob of getting two white socks in a row for all case and see which is 50%.

P(two w in a row| 2 white socks) = (2/4) * (1/3) = 1/6 => not two socks.
P(two w in a row| 3 white socks) = (3/4) * (2/3) = 1/2 => this is our answer.
Obviously, if there were 4 socks, we would have a 100% chance of getting two whites in a row. So as calculated, there must be 3 white socks.

- j-dw on Oct 13, 2012
0
of 0
votes

The probability is 0 as there is only 1 black sock.

Solution:
Assume there are k white socks and 4-k black ones in the drawer. =>
0.5 = P(2 white socks in a row) = k/4 * (k-1)/3 =>
k^2 - k - 6 = 0 =>
k = 3 is the number of white socks. qed.

- Alex on Oct 1, 2013

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