Question on probability using Bayes' theorem

Yes, this is correct.

The general form of Bayes' rule is

$$P(A_i|B)= \frac{P(B|A_i)P(A_i)}{\sum_jP(B|A_j)P(A_j)}$$

as you've used above.

Suppose 100x total students

Blue eyed =50x

Grey eyed =30x

Other eyed =20x

1st run selection :

Blue eyed =41x

Grey eyed =19.5x

Other eyed=10x

Not selected in 1st round

Blue= 9x

Grey=10.5x

Other =10x

P=(9x)/(9x+10.5x+10x)=.305