How To Solve Amazon's Pair Of Socks Interview Puzzle

This problem was part of a written interview test for Amazon in India. A drawer contains 12 identical black socks and 12 identical white socks. If you pick 2 socks at random, what is the probability of getting a matching pair?

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[MindYourDecisions]

Wow in just about one week you guys have captioned this video in English, AND it's been translated into Arabic and German! Captioning is a lot of hard work--I know I've done a few--and I'm really appreciative. I read that Youtube gives some rewards for doing captions, has anyone earned any worthwhile rewards yet? You guys are great, I have so many things to be thankful for this year!

[authorFreeman]

Applicants who got this right were put to work in the warehouse fulfilling sock orders.

[ElxXxObiwanek]

This was so easy I was starting to get paranoid if maybe I'm missing something. By the way who with even the slightest knowledge of how propability works would assume it's 50%... Also I think the better and faster method of considering it is: The first sock you pick doesn't matter which colour is it, but the second one must be matching. Since we've already taken out one of this color sock there are 11 left out of 23. So it's 11/23

[bobjordan]

I did it a bit different. We were only asked to get a matching pair. So whatever is picked first, be it black or white, means that on the second pick we have to pick what we picked in the first pick. The odds of getting the second sock to match the first pick is 11 out of 23. That equals 47.8%. After posting this I saw others did it this way too.

[puskajussi]

Answer is 0. I can tell from experience.

[jeffsurratt]

Good problem. It's easy for many of us that are used to thinking, but it's good for a lot of viewers to see the easier/basic stuff, too. So thanks for mixing up the difficulty level!

[JLConawayII]

The answer is I don't pick any socks, I just buy a new pair on Amazon. "You're hired!"

[YufaGaming]

For a matching pair you don't need to add a probability for Pr(bl) and Pr(wh). All you need to do is to calculate the 11/23. Since you can pick any color with your first pick - the question becomes "what is the probability that the next color is the same". Hence 11/23. Result is the same, it's just simpler.

[AuraRift]

Probability of picking a matching pair is 100% because I match my socks when I do laundry and roll them together. Too easy >_>

[dj_laundry_list]

I seem to have an infinite number of socks in my drawer, so the probability is 50%

[sietievdw]

I don, t mind if i wear black or white soks, so i pick 3 then i always have a pair in the same color.

[vickichamberlain]

At the Railroad we had a similar set of choices. To fix a broken rail at night you need what are called Angle Bars. These bars fit in the web of the rail and hold the bolts and rail to make a complete joint. Usually we would need 2 sets (4 bars) to cut out the defect and add a length of rail. The problem is that the shoulder of the bolts is oval and locks the blot from spinning when you tighten an 1 1/8in bolt. Most bars have the oblong hole to the right end of the bar then alternate oval, round, oval, round, oval, round. There are 6 holes, 3 round and 3 oblong in each bar. Once in a while you find and outlier and it has the oblong/oval hole on the left of the bar. When you put 2 oblong left bars together you make a good joint because every other bolt goes in from the oblong hole and comes out of the other bar through the round hole. So 2 Oblong right bars make a set and if you get an oblong left mixed in you can not make the joint safe because the oblong/oval holes line up with each other and only 3 of the bolts can be held fast. In the dark you always get an odd number of bars just incase you mix the oblong rights and oblong lefts. With an odd number you will always be
able to make a joint/pair.

[daggle]

the first sock doesn't matter anyway, only the probability for the second sock counts and that's your result.

[Nicholas-grpb]

Easy, 11/23. First sock can be anything then 23 socks left.
If first white, probability second white 11/23
If first black, probability second black 11/23
(ie 11/23 chance that the second sock is the same as the first)

[kenhaley]

Again, his explanation is far too complex. It should just be this:

After you pick the first sock there are 11 more socks of that color, and 12 of the opposite color. So the chances of picking another sock of the same color are 11 out of a total of 23, which equals approximately 47.8%. Done!

Why complicate things with the rest of that algebraic notation, confusing verbiage ("sampling without replacement"? shees!), separate consideration of the black sock case vs. the white sock case, etc. Keep it simple, I say.

[Abdurrehman-eenw]

this is straight forward Probability question, 24 socks in totals, you've picked X color now you can pick from other 11 of that color out of a total of 23 socks.
i.e 11/23 = 0.47
I didnt know they had redefined PUZZLE in the dictionary to this

[voteforno.]

The answer is 10/23 [correction, 5/11, see comments below] because after you pick the first sock, one of the remaining matching socks escapes.

[PaulMurrayCanberra]

Another way to think of this:

Number all the socks. Black even, white odd. Or black low, white high. Whatever. If you pick two numbers at random, there's a 50/50 chance of getting an odd-even pair. The problem is that the pairs 1:1, 2:2, 3:3 and so on are not pairs you can actually take from the draw. These invalid pairs are all matching pairs, so there are fewer possible matching pairs than 50/50.

[apxprdtr_mge]

For a brief moment, I was happy that I solved it in a few seconds, but then it hit me, it's really not exactly something to write home about.
Good puzzle though, always love the ones with probability, even though it's not my area of expertise.

[Nighteye]

You missed the trick to the question: the socks are identical, so there are no matching pairs. Your black or white socks will either be 2 left socks or 2 right socks, not a pair of 1 left sock and 1 right sock.