Question

A system was developed to classify an object that belongs to one of three classes. The system is trained using 100 objects that are already known by its class. From these 100 objects obtained information that 40 came from class A, 35 from class B, and the rest from class C.

a. If there is only information like the one above, then determine the probability of misclassification?

Answer 1

Objects in class A = 40

Objects in class B = 35

Objects in class C = 25

Total Objects = 40+35+25 = 100

Probability of choosing A, P(A) = 40/100 = 0.4

Probability of choosing B, P(B) = 35/100 = 0.35

Probability of choosing C, P(C) = 25/100 = 0.25

Probability of misclassification of A, P(wrong/A) = (100-40)/100 = 0.6

Probability of misclassification of B, P(wrong/B) = (100-35)/100 = 0.65

Probability of misclassification of C, P(wrong/C) = (100-25)/100 = 0.75

So, Probability of misclassification, P(wrong) = P(A)*P(wrong/A) + P(B)*P(wrong/B) + P(C)*P(wrong/C)

= 0.4*0.6 + 0.35*0.65 + 0.25*0.75

= 0.655