I doubt any of you mathfags will be able to solve pic related

oh didn't see your answer and indeed made me realise I don't know my squares, i counted 25 rather than 15 :
you're right, 105 120 thus he lost a white sock

however, I dare say you're quite troubling yourself, you just need to count when you take a not matching pair that is 2WB and say the probability is still 1/2 :

2WB/card( WuB2 \ diag) = 1/2

oh and everything is discrete so prob in this case is just counting measure.

On another note, it's been so long, how do you use latex in here already?

This dude is right

How can this be right.
If there are more black than white, then the chance of randomly drawing isn't 50/50

If I'm thinking about this correctly the probability of getting a getting two black socks does not have to be the same as getting two white socks. It can still average out to 50% chance of getting matching socks when picking them randomly.

Could you explain how you found 105 , 90 as a solution, I lost you on that step

Where did this expression come from?

You rearrange
[eqn] W (W-1) + B (B-1) = 2 W B [/eqn]

2b(b-1)+2w(w-1) = (b+w)(b+w-1)
(b-w)^2 = b+w
15^2=225
w = 105
b = 120
White sock was lost

I'll re write fully so that people see it more clearly :
In the following universe
[math]S = B \cup W \ \ \Delta = \{ (x; x) \in S^2 \}[\math]
[math] \Omega = S^2 \setminus \Delta [\math]
(because we can't take two times the same socks)
the random variable is then : I take a pair of socks (an elt in [math]\Omega [\math]) and determine weither they match or not (0 or 1) :
[math]X : \Omega \rightarrow \{ 0; 1 \} [\math]
of course it's indeed a random variable, because the tribe is the powerset, but let's not write every details. The probability measure is the counting measure (card of set divided by card of total).
Rather than calculating directly, let's calculate the probability of having two mismatching socks :
[math] P(mismatching \ socks) = P(X^{-1}(0)) = 1 - 0.5 = 0.5 [\math]
And you have two mismatching socks whenever the first is black the second is white or the contrary i e : [math] |B| \cdot |W|+ |B| \cdot |W| [\math]
Finally : [math] |\Omega| = (|B| + |W|)^2 - (|B| + |W|) [\math]
thus :
[math] \frac{ 2BW}{(B+ W)^2 - (B + W)} = 0.5 [\math]
[math] 4BW = (B+W)^2 - (B + W)[\math]
[math] (B+W) = B^2 + W^2 - 2BW [\math]
[math] B + W = (B - W)^2 [\math]
everything else has already been said : the sum is between 200 and 250 and a perfect square, and it is the difference in socks.