Question
Suppose that the reliability of a COVID test is
specified as follows: Of people having COVID, 90% of the test detect the disease but 10% go undetected. Of people free of COVID, 99% of the test are judged COVID–ive but 1% are diagnosed as showing COVID+ive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID test, and the pathologist reports him/her as COVID+ive. What is the probability that the person actually has COVID?Solution
Let E denote the event that the person selected is actually having COVID and A the event that the person's COVID test is diagnosed as +ive. We need to find P(E|A). Also, E’ denotes the event that the person selected is actually not having COVID. Clearly, {E, E'} is a partition of the sample space of all people in the population. We are given that P(E) = 0.1% = 0.1/100 = 0.001 P(E') = 1 – P(E) = 0.999 P(A|E) = P(Person tested as COVID+ive given that he/she is actually having COVID) = 90% = 90/100 = 0.9 and P(A|E') = P(Person tested as COVID +ive given that he/she is actually not having COVID) = 1% = 1/100 = 0.01 Now, by Bayes' theorem P(E|A) = [P(E) × P(A|E)]/[P(E) × P(A|E) + P(E') × P(A|E')] = [0.001 × 0.9]/[0.001 × 0.9 + 0.999 × 0.01] = 90/1089 = 0.083 approx.
- Statements: E < F > G; H < I ≤ F; E > D
Conclusions:
I. F > D
II. H < E
III. G < D Statements: O < P > Q; R < V ≤ P; O > N
Conclusions:
I. P > N
II. R < O
III. Q < N
Statements: I = H ≥ T = W ≥ M; N < L ≤ M = G ≤ K
Conclusions:
I. I > G
II. N < T
III. H ≥ L
Statements: M ≥ O ≥ P ≤ W, N ≥ K ≥ Y = M
Conclusion:
I. N > W
II. Y ≥ P
Statements:Â Â Â Â Â Â Â X @ Y % M % N; M $ P $ Z
Conclusions :     I. Y % Z               II. X @ N          �...
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and th...
Statements:
J ≥ F = P; F > S ≥ A; S ≥ B < C
Conclusions:
I. C > A
II. B < J
Statements: A > B ≥ C ≤ D; E ≥ F ≥ G = A
Conclusion:
I. E > D
II. D ≥ E
Statements: J > K = L ≥ N > M > O ≥ P
Conclusions:
I. K ≥ O
II. J = N
III. P < NIn the question, assuming the given statements to be true, find which of the conclusion (s) among given two conclusions is /are definitely true and the...
Relevant for Exams:
