Latest Elitmus Aptitude Question SOLUTION: 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)

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(#M40155909) ELITMUS Numerical Ability question Keep an EYE

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

Asked In Elitmus Rizul (8 years ago)

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Mallikarjuna Reddy  (8 years ago)

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

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Ravi Kumar Soni  (8 years ago)

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)

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dytort  (8 years ago)

20C2/20C4 = 99/323

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Souham Singh  (6 years ago)

Question is from Arun sharma quantitative, difficulty level 3 question number 45.

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shikha pandey  (8 years ago)

I could not read the solution.. it is not visible

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