Question

I have 10 socks in a drawer, some black and some white. If 2 socks are selected at random, the probability that they are both black is 1/3. What is the probability the 2 socks selected are not a matching pair? Assume each sock has the same probability of being selected

Answer 1

Let the number of black socks be n

P(2 black socks) = 1/3

n/10 x (n-1)/9 = 1/3

n(n-1) = 30 {we know that 6x(6-1) = 30}

n = 6

Nuber of black socks = 6

Number of white socks = 10 - 6 = 4

P(the 2 socks selected are not a matching pair) = P(first sock is black and second sock is white) + P(first sock is white and second one is black)

= 6/10 x 4/9 + 4/10 x 6/9

= 0.5333