math question

[Pierre.Suave]

if you had

18 red socks

24 white socks

8 blue socks

10 black socks

how many socks would you have to pull out of the drawer to get a MATCHING pair?

Must show your work to get credit.

[Betsy Ross]

1. 5

[Chan790]

2. 5.

There are 4 colors of socks, hence the 5th sock must match one of the first four drawn. The quantity of each color in the drawer is irrelevent and is included only to confuse the recipient of the question.

[jberryhill]

5. That's a really weird answer

If you pulled out a red sock, then why on your second pull, would you pull out anything other than a red sock.

You have made the classic "expert" error of reading conditions into the problem that were not stated.

The problem as stated does not say you can't see the socks in the drawer (a "blind draw" problem).

I can't imagine how you manage to get dressed in the morning, but I rarely have to make more than two attempts to get a pair of socks out of a drawer.

[Pierre.Suave]

9. you cant see the socks

thats why

it is a math problem, not a trick question.

[jberryhill]

19. Okay, so if I can't see the socks

Then I pull out 5 socks.

I know there's a matched pair in there somewhere, but I don't know which ones to put on my feet, since I can't see them.

I'm screwed. No matter what I do, I'll probably have mismatched socks and three other ones left on the floor.

Then my wife will yell at me.

[hvn_nbr_2]

37. Ha! Then my answer is 1.

I pin pairs of socks together with a safety pin so I don't have to match them up after the laundry. So if I reach into the drawer and pull out one sock, I have a matching pair.

[jberryhill]

3. 2

A pair of socks is 2 socks.

Is this a trick question?

Why would I pull a mis-matched pair out of the drawer?

Or did you mean to set some other conditions here?

I'm not blind.

[Pierre.Suave]

6. Assume it is dark and you cant see

the colors of the socks.

[jberryhill]

10. Oh - that's a DIFFERENT problem

The answers you get, depend on the question you ask.

I suppose next you are going to tell me that there are three drawers and one sock, and Monty Hall has me pick a drawer. Then, he opens an empty drawer and offers me an opportunity to change my choice.

Should I?

Your statement is STILL wrong, though, because you asked how many pulls for a "pair" not a "matched pair".

You want to try again?

[PBS Poll-435]

7. !

That's what I was thinking.

Sure, you got a pair, but they may be mis-matched.

[jberryhill]

11. Why would they be mis-matched

I can see colors and everything.

[PBS Poll-435]

17. Pull two socks out of a drawer, and you will have a pair

They might match (slim chance) or they won't.

Either way, you will have a "pair of socks."

[jberryhill]

20. Why would I pull a pair of mis-matched socks out of the drawer

If I pull two socks out of that drawer, I'd pick two of the same color.

Jeezus, how do you people get dressed?

[PBS Poll-435]

22. Like this

I brush my teeth.

I shave.

I pluck rogue eyebrows.

I exfoliate.

I shower.

I dry off.

I pick out my clothes.

I pull 2 socks out of my dresser-drawer.

I put on said clothes.

I style my hair.

I put in my contact lenses so that I can see what the fuck I am doing.










:P

[jberryhill]

25. I thought you pulled out five socks

Now I'm just confused.

I'm glad my wife started dressing me after mom quit.

[NightWatcher]

4. who keeps their socks in the drawer? mine are in the "clean pile" next to the bed

[The Velveteen Ocelot]

8. Two.

You'd have a pair; they just might not match.

[Pierre.Suave]

13. who would wear a mismatched pair?

Honestly? Who does that?

:P

[jberryhill]

15. You didn't specify a matched pair

You said, how many for "a pair".

That would be two socks.

I hope you aren't writing exam questions...

[The Velveteen Ocelot]

16. I would. But that's just me.

[madinmaryland]

12. TWO.

I see you changed it to a matching pair.

You only asked for a pair before you edited it!

[Pierre.Suave]

18. I did not think I would have to specify that

but I see the lounge smart-asses are in full force tonight...

:P

[madinmaryland]

21. What do you think we are? Freakin' mind readers?

:rofl:

[jberryhill]

23. Seriously

You have a drawer with pants.

How many pants do you need to pull out to get a pair of pants?

The question might as well have been "I'm thinking of a math problem. What's the answer?"

[JimWis]

14. 2

[pokerfan]

24. 5 at most

worst case is one each of the four different colors. The fifth draw will match one of the previous four.

[jberryhill]

26. Lemme ask you something

You park your car in a parking lot with 500 cars in it.

When you leave the store, just how many cars do you drive away in?

[pokerfan]

29. that's easy

(499/500)⁰=1

:shrug:

Here's one for you:

1. There are five houses.
2. The Englishman lives in the red house.
3. The Spaniard owns the dog.
4. Coffee is drunk in the green house.
5. The Ukrainian drinks tea.
6. The green house is immediately to the right of the ivory house.
7. The Old Gold smoker owns snails.
8. Kools are smoked in the yellow house.
9. Milk is drunk in the middle house.
10. The Norwegian lives in the first house.
11. The man who smokes Chesterfields lives in the house next to the man with the fox.
12. Kools are smoked in the house next to the house where the horse is kept.
13. The Lucky Strike smoker drinks orange juice.
14. The Japanese smokes Parliaments.
15. The Norwegian lives next to the blue house.

Now, who drinks water? Who owns the zebra? Etc.

(In the interest of clarity, it must be added that each of the five houses is painted a different color, and their inhabitants are of different national extractions, own different pets, drink different beverages and smoke different brands of American cigarettes. In statement 6, right refers to the reader's right.)

[jberryhill]

30. Flvegan drinks the water

And he better hurry up before it expires.

[The Velveteen Ocelot]

27. 8.

That's the smallest number of any one color.

But what kind of a slob would put their socks in the drawer without sorting them and rolling them into balls so you don't have to do weird math to get a pair of matched socks?

[jberryhill]

28. Hey, can I borrow you for a while

I have some laundry to put away.

[tjwmason]

31. None or 2

Socks only get as far as a drawer if they've been matched into pairs. Thus socks in drawer are matching (hence 2), or socks aren't in the drawer (hence none).

[jberryhill]

32. Holy cow, you're right - it IS Zero

I'm already wearing a pair.

I do not need to pull any socks out of the drawer to get a pair.

[Rabrrrrrr]

33. Whoops. Double posted.

[DS1]

34. That's what a Butler is for, ass.

[Rabrrrrrr]

35. Assuming you mean a matching pair outside the drawer, and that one is drawing blindly,

and that the socks are not already joined together in pairs, and that by matching you mean "of the same color" not just colors that go well together, and assuming you are drawing socks one at a time, then the answer is:

minimum of 2, maximum of 5

[jberryhill]

36. Still missing a condition

The question, as slyly edited, was how many socks do you need to get "a matching pair".

It did not specify "a matching pair of socks from among those selected from the drawer".

If you already had, for example, a matching pair of socks on your feet, a matching pair of shoes, or even breasts or testicles, then the answer remains zero.

[RandomThoughts]

38. Best guess.

Here is my guess, since the question is how many, but randomness in the drawing is assumed the real answer should be what are the odds of it taking 1 draw, 2 draws, 3 draws, 4 draws, or 5 draws.

This does add to the question, but it is best way I can think of answering the question.

Answer:
1st draw 0% chance
2nd draw 28.2% chance
3rd draw 31.8% chance
4th draw 35.3% chance
5th draw 4.7% chance

Work shown, awaiting extra credit :)
60 total socks R means red sock, W means white sock, B means blue sock K means Black sock.

1st draw,
30% chance of R
40% chance of W
13.3% chance of B
16.7% chance of K

0% chance of match

2nd Draw

if R was first draw.(30%)
28.8% chance of second draw being R.
This will occur-----------------------8.4% of the time.

if W was first draw(40%)
39% chance of second draw being W
This will occur-----------------------15.6% of the time

if B was first draw(13.3%)
11.9% chance second draw being B
This will occur-----------------------1.6% of the time.

if K was first draw(16.7%)
15.3% chance of second draw being K
This will occur-----------------------2.6% of the time.

So probability of match on second draw is 28.2%

If no match, we must draw 3rd time, but their are many combinations.
if R first draw(30%)
----40.7% chance of W draw on second
--------(17 + 23) / 58 or 66.7% chance of match draw.
This will occur------------------------8.1% of the time.

if R first draw(30%)
----13.6% chance of B draw on second
--------(17 + 7) / 58 or 41.4% chance of match draw.
This will occur------------------------1.7% of the time.

if R first draw(30%)
----16.9% chance of K on second draw
--------(17 + 9) / 58 or 44.9% chance of match draw.
This will occur------------------------2.3% of the time.

.........................................................
if W first draw(40%)
----13.6% chance of R draw on second
--------(23 + 17) / 58 or 66.7% chance of match draw.
This will occur------------------------3.6% of the time.

if W first draw(40%)
----13.6% chance of B draw on second
--------(23 + 7) / 58 or 51.7% chance of match draw.
This will occur------------------------2.8% of the time.

if W first draw(40%)
----17% chance of K on second draw
--------(23 + 9) / 58 or 37.9% chance of match draw.
This will occur------------------------2.6% of the time.

.........................................................
if B first draw(13.6%)
----30.5% chance of R draw on second
--------(7 + 17) / 58 or 41.4% chance of match draw.
This will occur------------------------1.7% of the time.

if B first draw(13.6%)
----40.7% chance of W draw on second
--------(7 + 23) / 58 or 51.7% chance of match draw.
This will occur------------------------2.9% of the time.

if B first draw(13.6%)
----16.9% chance of K on second draw
--------(7 + 9) / 58 or 27.6% chance of match draw.
This will occur------------------------0.6% of the time.

.........................................................
if K first draw(16.7%)
----30.5% chance of R draw on second
--------(9 + 17) / 58 or 44.9% chance of match draw.
This will occur------------------------2.3% of the time.

if K first draw(16.7%)
----40.7% chance of W draw on second
--------(9 + 23) / 58 or 37.9% chance of match draw.
This will occur------------------------2.6% of the time.

if K first draw(16.7%)
----13.6% chance of B on second draw
--------(9 + 7) / 58 or 27.6% chance of match draw.
This will occur------------------------0.6% of the time.

Match found on 3rd draw will occur 31.8% of the time.

So
1st draw 0% chance
2nd draw 28.2% chance
3rd draw 31.8% chance

Not doing 4th draw, but I think you could find odds of 1 of each being drawn, then reverse that, or continue same method.

What are the odds of drawing one of each, the only way to get a no match.
you could figure each combination with 60-59-58-57 but pretty sure they average out
so you get 16 possiblities of 1 each, just figuring them all at 58.5 average total socks
to get 16 * odds of 1 each.

RWBK, WBKR, BWRK, etc...
R 18/58.5(30.8%) * W 24/58.5(41%) * B 8/58.5(13.7%) * K 10/58.5(17.1%)

Multiply this by the 16 different sequences possible * 16

4.7% of the time 4 draws will get one of each so chance to get to 5th draw is only 4.7%

So
1st draw 0% chance
2nd draw 28.2% chance
3rd draw 31.8% chance
4th draw 35.3%(100 - 28.2 - 31.8 - 4.7)
5th draw 4.7%

[Frosty1]

45. You just gave me a headache

:crazy:

[Dr. Strange]

39. Locking.

Pigeonhole Principle Thread. Please keep all posts on Ramsey Theory in the Entertainment Forum. Thank you.


(The answer is 5: the socks are the pigeons and the colors are the pigeonholes.)

[CreekDog]

40. Locking

Thread locker wannabe is no longer with us.

[Pierre.Suave]

44. smartass

:P

[Deja Q]

41. 1

I don't wear socks.

Well, not on me feet...

:yoiks:

[flvegan]

42. Who the hell has 30 pairs of socks?

[Pierre.Suave]

43. You Dont?

:shrug: