Drat, I typed something in and somehow it got lost.
Here's the gist of it.
It often helps to list all of the possible outcomes with their associated probabilities, their sum should equal 1.
If it does, you can be reasonably sure that you haven't missed anything.
So, we have
O, O = 3/10 * 2/10 = 6/100,
O, N = 3/10 * 7/10 = 21/100,
O, S = 3/10 * 1/10 = 3/100,
N, O = 7/10 * 3/10 = 21/100,
N, N = 7/10 * 6/10 = 42/100,
N, S = 7/10 * 1/10 = 7/100.
Total = 100/100, tick.
The probability that the second coin is an old Peso is 6/100 + 21/100 = 27/100.
If we disagree somewhere then at least we should be able to see where the disagreement is.