Question

In your top dresser drawer there are 6 blue socks and 10 grey socks, unpaired and mixed up. one dark morning you pull two socks from the drawer (without replacement, of course!). what is the probability that the two socks match?

Answer 1

The probability that the two socks match can be translated into the probability of getting two blue socks or two grey socks.
The combination ways for taking 2 socks from 16 socks would be: 16C2= 16!/2!14!= 120
Way to get 2 blue socks of 6 blue sock: 6C2= 6!/2!4!= 15
Way to get 2 grey socks of 10 grey sock: 10C2= 10!/2!8!= 45

Then the probability is: 15+45/ 120= 60/120= 1/2