Question

A man wears socks of two colours – Black and brown. He has altogether $20$black socks and $20$brown socks in a drawer. Supposing he has to take out of the socks in the dark, how many must he take out to be sure that he has a matching pair?
$
  (A)\,3 \\
  (B)\,20 \\
  (C)\,39 \\
  (D)\,None\,\,of\,\,these \\
 $

Answer 1

Hint: For this problem one sock is drawn one after another, might be socks are of the same colour or different color. To get the same colour sock man has to draw another sock and proceed in the same way till he gets his pair of the same socks.

Complete step-by-step answer:
Here, in this problem man has two colour socks. $20$Socks are of black colour and $20$ socks are of brown colour.
We have to find a minimum number of draws of socks so that he has matching socks either of black colour or of brown colour.
As man draws out socks in dark, so in his first draws might be he draws out black colour sock or brown colour sock. As, there are only two colour socks.
Let us assume that in his first draws he got a black colour sock.
Now, to complete his pair he has to draw on more time.
In his second draw he might get a black colour sock or brown colour as he is pulling out in dark.
Let's say he got a brown colour sock in the second draw then he got a pair of socks of different colour. Also, there is a chance he might take out a black colour. Then in this case his pair of socks will be completed but as getting out of two consecutive black socks if not possible every time.
So, let man give another try. In his third draw he will get a sock of either black colour or brown colour.
If he gets black colour sock in the third draw then in combining first and third draw he got his pair of balck colour socks to wear.
 But if in the third draw he gets brown colour socks then in combining second and third draw he got his pair of brown colour socks to wear.
Same procedure can also be applied if in his first draw he gets brown color sock.
Therefore, from above we see that to surely get a pair of socks of the same colour, man has to draw socks minimum three times.
Hence, from given four options the correct option is (A).

So, the correct answer is “Option A”.

Note: Might be in the first two draws a man got socks of the same colour but this will not happen every time. So, to get a sure and accurate pair of socks of the same colour to wear every time, minimum $three$ draws required.
Also, there will be another case in which he gets the same colour socks in all three draws but as mentioned above this will happen sometime or not some time. Hence, to get an accurate pair of socks of the same colour minimum three draws required as we disuse above.