There are 10 pair of socks in a cupboard from which 4 individual socks are picked at random. The probability that there is at least one pair is:
a) 195/323
b) 99/323
c) 198/323
d) 185/323

• probability is 1-p(drawing four socks which ar different)
  p(drawing four socks different) (20/20)*(18/19)*(16/18)*(14/17)=>224/323
  so probability is 1-224/323=>99/323
  option b
• 8 years agoHelpfull: Yes(30) No(4)
• whenever 4 socks are picked
  there can be either
  0 pair or 1 pair or 2 pair
  
  so p(0 pair) + p(1 pair) + p(2 pair) = 1
  we have to calculate p(1 pair) + p(2 pair)
  so it is equal to 1 - p(0 pair)
  
  p(1 pair) + p(2 pair) = 1 - p(0 pair)
  
  so.. p(0 pair) can be understood as
  
  _ _ _ _
  
  Gap 1 can be filled in 20c1 ways but there are pairs
  so gap1 20c1/20c1 , similarly
  gap 2 18c1/19c1, 18 because 1 is chosen in gap1 so... if we say 19 ...then there can be pair
  gap 3 16c1/18c1, 16 because 2 are chosen in gap1, gap2
  gap 4 14c1/17c1
  
  p(0 pair) = 20c1/20c1 * 18c1/19c1 * 16c1/18c1 * 14c1/17c1
  and thus total required ans is = 1 - p(0 pair)
• 8 years agoHelpfull: Yes(10) No(4)
• 20C2/20C4 = 99/323
• 8 years agoHelpfull: Yes(4) No(18)
• Question is from Arun sharma quantitative, difficulty level 3 question number 45.
• 6 years agoHelpfull: Yes(4) No(3)
• I could not read the solution.. it is not visible
• 8 years agoHelpfull: Yes(1) No(4)