Question

5. A medical test for malaria is subject to some error. Given a person who has malaria, the probability that the test will fail to reveal the malaria is 0.06. Given a person who does not have malaria, the test will correctly identify that the person does not have malaria with probability 0.91.

1. (a) If someone has malaria, what is the probability that the test will identify that person as having malaria?

2. (b) Suppose three unrelated individuals who are not infected with malaria take the test. What is the probability that at least one of the three individuals will be identified by the test as having malaria?

3. (c) In a particular area of a particular country, 20% of the population suffers from malaria. If a random person from this area is tested and his test results indicate that he has malaria, what is the chance that he actually has malaria?

Answer 1

Let the Events be: M person has malaria P Test detects Malaria's presence Given : Bl pel M) -0.06 a PRC PIM) -0.94 +1 -0.06 Prl pel Mc) = 0.91 Prept MC) = a) 1- 0.91 = 0.09 Pec PIM) = 1- P&C palm) 1-006 test correctly indicates presence

(6) Let Events be positive person = PI: Person I tested P2: Person 2 tested positive Psi Person 3 tested positive Prat least one tested tie) I- Prl all ove) I- Prl pic Paco P3) 1- PRC PIC) Pr CP2 C) Pr CP39 independence PRC PC/MC) Pr (229 Pal Ps) => Read prob 1-10.9113 ñ0.246 Prl PC) 1-6091:10:91).691

(e) BCM/P) Read prob PXCP) PR (M) P&(PIM) t Pa(MC) PRCPMG - 10.2) (0.94) + (0.8) (0.09) PXC MI РАСМЛР) РАС Р) 012)(0:94) 0-2)(0.9+) +(0-8)(0:09) 0.188 0 723 0.26