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Kevin is trying to find a white sock in his drawer. He has 16 white socks, 4 brown socks, and 6 black socks. What is the probability that he pull out either a black or brown sock, puts it back, and then pulls out a white sock?

A9/13
B20/13
C40/169
D96/169

Verified Answer :

AL2006

We have to assume that he does all this with his eyes closed, and so his selections are completely random.

-- There are 26 socks in the drawer all together.
-- 10 of them are black or brown.
-- So the probability that he pulls out
       either a black sock or a brown one is 

                                             10/26 = 5/13 = about  38.5% .

-- He puts it back, so there are still 26 socks in the drawer.

-- 16 of them are white.
-- So now, the probability of pulling out a white one is

                                             16/26 = 8/13 = about  61.5% .

The probability of the whole process happening
just exactly as you described it is

                       (10/26) x (16/26)

                 =    (5/13)  x  (8/13)

                 =    (40) / (13²)  =  40/169  =  about  23.7% .

Quick check:

 We got  38.5% the first time, and  61.5% the second time.

            (38.5%) x (61.5%) 
      
       =  (0.385 x 0.615) 

       =  0.2367 ==> 23.7%  <== yay!       that's good enough for me  
                        

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