The numerator of the desired probability is the number of ways
to choose two blues and two reds:
5 blue marbles choose 2 in 5C2 = (5∙4)/(2∙1) = 20/2 = 10 ways.
2 red marbles choose 2 in 2C2 = (2∙1)/(2∙1) = 2/2 = 1 way.

So the number of ways to choose 2 blues and 2 reds is:
(5C2)(2C2) = 10∙1 = 10 ways. 

So the numerator of the desired probability is 10.

The denominator of the desired probability is the number of ways
to choose ANY 4 marbles:

4+5+2+3 = 14 marbles choose 4 = 14C4 = (14∙13∙12∙11)/(4∙3∙2∙1) = 24024/24 = 1001 ways.

So the denominator of the desired probability is 1001.

The desired probability is therefore 10/1001. 

Edwin