The four probabilities given as premises are inconsistent. The first three determine the fourth. (Also, there’s an arithmetic error in the p(G|M) calculation, as pointed out by Bucky.)
If this feels confusing, I suggest drawing a Venn diagram or something. If you have a box of area 1.0, containing a blob M of area 0.9 and another blob G of area 0.05, such that G is almost entirely inside M, then...
The four probabilities given as premises are inconsistent. The first three determine the fourth. (Also, there’s an arithmetic error in the p(G|M) calculation, as pointed out by Bucky.)
Given
p(M) = 0.9
p(G) = 0.05
p(M|G) = 0.99
it must be that
p(M|-G) = (p(M) - p(M,G)) / (1 - p(M,G) - p(-M,G)) = 0.8505 / 0.95
which is approximately 0.895263. Not 0.02.
If this feels confusing, I suggest drawing a Venn diagram or something. If you have a box of area 1.0, containing a blob M of area 0.9 and another blob G of area 0.05, such that G is almost entirely inside M, then...