a drawer contains unsorted 20 black socks, 20 brown socks, 20 blue, and 20 grey socks.?

Question

how many socks must be chosen in order to be certain that
A. there are two of the same color?

B. that there is either a pair of brown socks or a pair of black socks?

please explain how you got the answer.

Answer 1

A 5
B 43

A. is simple - if there are 4 different colors, the 5th MUST match one of the others.

B. Although highly unlikely, it is possible that the first 40 socks chosen are blue or grey. If you can pull that off, you should be in Vegas and forget about sorting socks! The next two socks may be one brown and one grey. The next (43rd) sock HAS to be brown or black.

Or just do like me - dark blue, black - nobody's gonna look that close to notice they don't match! :)

Answer 2

A. You must pull 5 socks to be sure you've got two of the same color, since 4 (1 black, 1 brouwn, 1 blue, 1 gray) is the maximum number you can have without a duplicate.

B. To be sure you've got a pair of brown or black...
it is possible to pull out all of the blue and gray first, so that's 40
now there are only brown or black socks left, so pulling 3 socks out of a drawer with only two colors of socks in it guarantees a matching pair.
so 43 socks to guarantee pair of brown or black

Answer 3

A: 5 if you pulled a new color each time (IE Black Brown Blue Grey Black) on the 5th try you would repeat and guarantee 2 matching.

B: Not enough info for some variations but I assume you mean that we are basing this on the question above. Therefore 50% there are only 4 colors so the probability of having 2 of those colors is 1/2

Answer 4

A. 5 -There are 4 colours (dont worry about the numbers/20s). Now lets say that at you are unlucky and in the first 4 goes you pick different colours. Yet in your 5th go you will pick up any colour, whatever it is, it will match at one of the previous 4.

B = 43. If you are unlucky, you'll get all the blues and all the greys first, so 40 goes are gone. That leaves black and brown only now. Now if you pick 2, and you are unlucky, you may still get no pair, yet after that the next one will definately make a pair, so 3rd after 40.

Answer 5

A. 5 If the first 4 socks you pick are black, brown, blue, and grey, you don't have a pair. But then the 5th sock has to match one of those.

B. 43 If you first pick all 20 blue socks, then all 20 grey socks, then brown on your 41st try and black on your 42nd try, you still don't have a pair of brown or black. But for your 43rd try, all that is left is brown or black, so one of them will have to pair up.

Answer 6

the most socks you could get without a match is one of each color, for a total of 4 socks. the 5th sock would be a match to one of them

in an extremely rare case, you could pull all of the blue and grey socks first, then one black one and one brown one. the 43rd sock would guarantee a brown or black match

Answer 7

I think your answer is 5. If you chose 4 socks and all 4 happened to be different colors then the 5th sock has to match one of the colors.

Answer 8

3. the two your first 2 socks will experience, or they are going to be diverse. yet then the 0.33 sock will experience the two the 1st one you pulled or the 2nd you pulled.