Probability of picking socks out of a drawer

Question

There are eight red socks and six blue socks in a drawer. A sock is taken out, its color noted, and is tossed aside. This procedure is performed three times. Let R be the random variable 'number of red socks taken'. Determine the probability distribution of R.

Answer 1

P(0 reds, 3 draws) = 6C0•8C3 / 14C3

 

P(1 red, 3 draws) = 6C1•8C2 / 14C3

 

P(2 red, 3 draws) = 6C2•8C1 / 14C3

 

P(3 red, 3 draws) = 6C3•8C0 / 14C3