Question

2. A rare disease affects 1% of the population. A test has a sensitivity of 98%, i.e., it will give a positive result 98% of the time that a person actually has the disease. The same test also has a specificity of 95%, i.e., it will give a negative result 95% of the time when a person does not have the disease. Denote the event that a randomly person has a disease by D, and the event that a randomly selected person has a positive blood test by T. (a) Express the given information in probability notation. (b) Calculate the probability that a randomly selected person has a positive blood test. (c) Calculate the probability that given a randomly selected person has a positive blood test that they have the disease. 3 2 2

Answer 1

T={ selected person hala positive blood test la) person 1% of p-pulata 001 0.99 Diseases they Disease lowe Di Da test giney consertdesut For positive results (098) test gives wrong result negative resents = (1-0.95 = 0:05) for ib) PLU)= 0.01%0.98 + Digg xo'05 = D'0593 593 10,0vo means out of 10,000 person. tested by kit, only 593 declared positive blood test. 10) PC actually positue ) = P( DA) O'Olx0.9 g 00593 0165.