This problem is easy to define, but I'm not finding it easy to solve...

Take some bags of mixed sweets with three different flavours: cherry, lemon and apple.

The number of each type of sweet in each bag is normally distributed.

The means are:

cherry 10

lemon 15

apple 7

They all have a standard deviation of 3.

How can I calculate the probability that most of the sweets in any given bag will be cherry?

Any help would be very greatly appreciated, however general or specific.