MadSci Network: Engineering

Re: How come socks often get lost in the dryer?

Date: Sat Mar 23 08:21:13 2002
Posted By: Eric Maass, Director, semiconductors / communication products
Area of science: Engineering
ID: 1016854628.Eg

The basic problem is simple:

there are two many 1 to 1 matchings, and so too many ways that at least 
one of a pair will be missing.

One of the pair can be lost  in one of several places:
a) when you take them off and drop them on the floor
b) when you move things around on the floor
c) when you scoop them up and drop them in the laundry enclosuer
d) in the laundry room
e) in the washer
f) in the dryer

Naturally, messier places make it easier for a lost sock to find a hiding 
place. So, if the floor of your room is messy -- well, it can be the safe 
haven for lots of errant socks.

Anyway, let's go through the probabilistic math:

If you only had one pair of socks, and the chance of losing one of the pair 
was, say, 5%...then there are two ways you could have a missing sock:
you could be missing the first or the second sock. The probability of not 
missing a sock is .95 x .95 = 90.25%, so there is a 9.75% chance of 
missing a sock.

Now let's imagine you have two pairs of socks, each matched.  Because 
each pairs of socks are matched, losing any one of the four socks causes 
a problem. So, the chance of not missing a sock is .95^4 = .8145, giving 
a19.55% chance of missing at least one sock and therefore having the 

With 4 pairs of socks, the probability of having this problem goes to 34%, 
and with 8 pairs of socks, the probability goes to 56%.

So, with 8 different pairs of matched socks, you are more likely than not to 
have the problem of  thinking "the dryer ate my sock".

Now -- what happens if you don't buy MATCHED socks? What happens if 
you buy 8 pairs of socks, all of the same style and color?

Then, you no longer have to spend time finding the matched colored/style 
socks...and you no longer get frustrated when you can't find the other blue 
pair of socks among all the greys and blacks and such.

Anyway -- here are two sites on this intended to explore the 
humor involved in this problem, the other elaborating on the efficiency 
involved in the solution proposed above:

The Bureau of Missing Socks

Buying a pair of socks is foolish

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