Question

In a drawer, there are 13 pairs of socks, 6 of which are white. If you randomly select two pairs of socks, whatis the probability that both are white? Express your answer as a reduced fraction.

Answer 1

`(5)/(26)`

1) Since there are 13 pair of socks and 6 of which are white, then 7 pairs are colored pairs.

2) So, by the Fundamental Principle of counting and there was no replacement after the second withdrawal, we can write:

`P=(6)/(13)\cdot(5)/(12)=(30)/(156)=(5)/(26)`

Note that in the first ratio, we've got the favorable events over the total number of socks. Since one was already taken in the second withdrawal we need to subtract one from the total number of socks and another of white ones.