There are classes A,B,C,D,E. Variable x has different means for each of these classes, but there is overlap in the range of x among classes. Item counts are different between classes, eg. there are many more A's than B's etc. Given an item with a known value of x but unknown class, how do I calculate the probability of it falling into class A vs. class B vs. class C etc.
eg. If x is close to the mean value for class C, there may be 60% probablity of this item falling into class C, 20% for class B, 10% for class D, 7% for class A and 3% for class E.