Socks Story
John Bayleaf often wears odd socks, and this afternoon was no exception. He tells me that he keeps all his socks in a bottom drawer and that when he dresses he removes a pair at random.
If he has four pairs of socks: one black, one white, one red and one blue. How many days per week on average will he be found wearing a matching pair?
If he has four pairs of socks: one black, one white, one red and one blue. How many days per week on average will he be found wearing a matching pair?
Labels: logic, mathemagic
posted by Rajesh Lal at
9:15 PM
8 Comments:
does he put back the socks in the drawer after wearing them?
if so, approximately one day every week since after he removes one sock, there are 7 left to choose from, 1 of which is the right color, giving a 1/7 chance for him to pick the right colo(u?)red sock
But then again, if he remoes a pair at random, does that imply that the socks are all paired up already which would in turn mean that he wears a matching pair every day.
OK. Assuming he doesn't put his dirty socks back into the drawer, then on Monday, he has a 1/7 chance to wear a matching pair, Tues is a 1/5 chance, Wednesday is a 1/3 chance, and Thursday is a ...uh... Never mind.
OK On Friday he better be able to wear a matching pair, because even though they are dirty, he should be able to see his previous mistakes and learn from there.
Saturday & Sunday, he wears sandals.
This riddle has too many unknowns. Does Mr. Bayleaf put his dirty socks back in the drawer to be reused? Does he keep them paired so he will always pull like socks, or is it just a mess in his drawer? Does he go without socks on the last three days of the week? I like riddles that don't leave any variables like this.
That being said. If he puts his socks back in the drawer everyday he has a 1/7 chance of getting a pair (assuming he doesn't keep them paired), thus on average 1 day a week he will be paired correctly. If he doesn't put them back, the calculations get a lot more complicated and statistically, he would have no days of correctly paired socks.
The way the way the problem is stated John has four pairs of socks and pulls a pair, each day, at random. The problem also states, the pairs are of the same color. So if John has four pairs of sock he will be wearing matching sock on four days of the week. Bare feet the other 3 days, unless the sock are washed regularly.
The statement that John wears odd sock is because they do not match the clothing he is wearing at the time.
Charlieo
He can buy more socks at http://jumpingsocks.com
approximately one day every week
how that
at first there is 8 choice then we have 7 choice so we have 8 X 7 =56 probabilities and there is only 4 X 2 pairs so the events we want is
8/56= 7
so the right answer is 7 it is math
to kindman:
you must be wrong because the only time you put 8 into 56 is when 8 is the denominater and 56 isthe numerator...so it isnt math!
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