The total number of possible sets is given by C(10, 4) = 210
And the ones we are interested in contain 2 white ones chosen from any 5 white ones and 2 black ones drawn from any 5 black ones
So we have
[ C(5, 2) * C(5, 2) ] / C(10, 4) = [ 10 * 10 ] / 210 = 100 / 210 = about 47.6%
