Problem:
There are 6 pairs of black socks and 6 pairs of white socks.What is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness.
This question was asked in Aamaon.
Solution:
Ways to pick any 2 socks from 24 socks = 24C2
Ways to pick 2 BLACK socks from 12 BLACK socks = 12C2
Probability of picking 2 BLACK socks (P1)= 12C2 / 24C2 = 66/276
Probability of picking 2 WHITE socks (P2)= 12C2 / 24C2 = 66/276
Probability of picking any 2 same color socks = P1+P2 = 66/276 + 66/276 = 11/23
hey selecting a white/black socks z 1/2 ri8 (12/24).
n selecting same color socks agn ll be 11/23
so probability ll be 11/46 right correct me if i am wrong
so it will be (11/46)*2 as white or black 11/23
ended up with same answer
the probability of selecting 1 from 6 pairs (12) black socks and 1 from 12 white socks then forming 0 pair is P(X=0)= 12*12/24C2
so the prob. of forming 1 pair, regardless of color, is 1-P(X=0) = 1- 12*12/24C2 = 11/23
but in the first place we have to assume all socks of the same color are identical
Your calculation is too difficult. Here is a simpler reasoning. You just pick the first sock (without caring which one or which color it is). There are 23 socks left with 11 of the same color as of the first sock. So there is 11/23 chance to make a pair. No need to analyze black or white separately.
Nobody has asked if these socks are already paired? Surely nobody puts single socks away…
Daniel’s solution is the most elegant. But lets try this. We have a drawer with 30 socks in it. They are selection of five random colors. What’s the chance of there being 15 pairs?