Seemingly simple probability question...

This looks to be pretty straight forward, but I am not getting the right answer...

300 chickens are in a barn. 63 are brown roosters and 77 are black roosters. 64 are brown hens and 96 are black hens. So, there are a total of 140 roosters and 160 hens, also there are 127 brown chickens and 173 black chickens. If one is chosen at random, what is the probability that it is a brown hen.

When I worked this through, I took (64/160)( 160/300) and came up with .213333333333...

Am I on the right track here?