A sock drawer contains five blue socks and eight black socks

A sock drawer contains five blue socks and eight black socks. If you reach into the drawer and choose one sock, then, without replacing the first sock chosen, you choose a second sock, what is the probability that you will get:

(a) a pair of black socks      

(b) a pair of socks which matches,

(c) two different colored socks?

Solution

(a) P(a pair of black socks) = P( first sock is black)* P( second sock is black)= (8/15)*(7/14) = 4/15 = 0.26667

(b) a pair of socks which matches= P(a pair of black socks)*P(a pair of black socks)

from part (a),  P(a pair of black socks) = (8/15)*(7/14) = 4/15 = 0.26667

similarly,  P(a pair of blue socks) = P( first sock is blue)* P( second sock is blue)= (5/15)*(4/14) = 2/35 = 0.05714

P(a pair of socks which matches) = 4/15 + 2/35 =  0.26667+ 0.05714 = 0.32381

(c) P(two different colored socks ) = 1 - P ( a pair of socks which matches) = 1 - 0.32381= 0.67619