Assuming the probability of both marbles being red is 2/15, the solution can be found as follows:
Let r be the number of red marbles. The probability of the first marble chosen being red is r/10. If the first marble chose is red, the probability of the second marble chosen being red is (r - 1)/9. The probability of both marbles being red can be expressed as:

This can be rearranged to give the quadratic equation:

which has the positive solution r = 4.
The answer is: there are 6 blue marbles in the bag.