There are 24 black socks and 18 blue socks. What is the probability of 2 draws being black?

Hello brandi

In the first draw you have to draw a black sock from 24 black and 18 blue socks. Total 42 socks.
The chance on a black sock is 24/42 x 100% = 57,142857%

In the next draw you have to draw a black sock from 23 black and 18 blue socks. Total 41 socks.
The chance on a black sock is 23/41 x 100% = 56,09756%

The chance on 2 black socks is therefore 24/42 x 23/41 x 100%= 32,055748%

If I may expand on Sarnian's fine explanation. Using combinations, we can set it up as:

\frac{C(24,2)}{C(42,2)}=\frac{92}{287}\approx .32055

That is, we are choosing 2 from the 24 black out of 2 from the total of 42.

Which agrees with Sarnian.