This is a question of permutation and combination ... in fact, permutation and combination are often inseparable.

First of all, the probability of getting the red ball for the first time is 3/(n+3);

Then the probability of getting the white ball for the second time is n/(n+2);

These two steps are gradual. So p (x = 2) = 3/(n+3) * n/(n+2) = 7/30 ... (1).

After simplification, 90n = 7N 2+35N+42, 7N 2-55N+42 = 0 (7N-6) * (n-7) = 0.

Because n is a positive integer, it is obtained that n = 7；;

In fact, when the equation is 1, it can be seen that 3n is a multiple of 7, which means that n must be a multiple of 7.