Question

Question # B.2 In Fig.B.2 below, suppose C denotes cancerous state and the marginal (prior) probability of occurrence of C is: P(C,-0.01; and, C denotes the non-cancerous state Further, if the medical treatment is pursued, it is denoted by the state, T; and, when the medical treatment is not administered, it denotes the state, T In relevant medical diagnostic and treatment procedures, there are two possible errors that may occur: Type I and Type II errors and their corresponding conditional probabilities are indicated in the state-diagram/matrix shown below. Types of errors denoted bv: X Probability States of error 0.02 0.05 TİTİ Error XType I Type II Specifving the underlving reasons clearly, answer the following: (a) With reference to details in Fig. B.2, define the following probabilities p(TC), p(UC), p(Т / C) and p(Т /C) between event sets: { C ,C) and { T ,T}; and, explain each of them (b) Determine the following probabilities: p(T) and p(T) using Bayes' rule; and, define/explain these two probabilities Fig. B.2 Useful hints/formulas The chance of occurrence of an event B, given that A has occurred or the chance of occurrence of event A, given that B has occurred, the joint occurrence can be written in a generalized form: P(AB) P(A)P(BIA) P(B)P(AB) Answer hint: { p(Т )-p(T /C) x p(C) + p(T / C)x p(C )-0.0293) 1. 2.

Answer 1

of error (given,in rPr 0.99 0.55 C. О.DS F4,3 PT) o 0202 PIT)つ 1-1-0293