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Interview Question

Options Trader Interview London, England (UK)

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?

Interview Answer

5 Answers


There is zero probability of pulling two black socks.

Interview Candidate on Jul 21, 2010

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

Anonymous on Aug 23, 2012

Above meant to say: Has the same probability

Anonymous on Aug 23, 2012

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

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

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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