there are 4 white socks and 4 black socks. You randomly divides socks into pairs. What is the probability that each pair consists of 2 socks of the same colour? Express answer as a fraction.
I have no idea where to even start.
There are a total of 8 socks: 4 white and 4 black. Two are randomly selected. Therefore, 8C2 or C(8,2) = 28
Out of 4 white socks, 2 white socks can be selected in 4C2 ways or C(4,2) = 6.
Out of 4 black socks, 2 black socks can be selected in 4C2 or C(4,2) = 6.
Total number of ways of selecting the same color: 6 + 6 = 12.
Probability of getting both socks of same color = 12/28 = 3/7
Alternatively, you can say there are a total of 8 socks of which 4/8 are white and 4/8 are black. To find the same color:
White socks: (4/8)*(3/7) = 3/14
Black socks: (4/8)*(3/7) = 3/14
Then, add the two probabilities: 3/14 + 3/14 = 6/14
Reduce 6/14 = 3/7 which is the same answer as above.