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.
Average of 20 numbers is 90. Average of first 8 numbers is 103 while average of last nine numbers is 40. If ninth number is 25% less than the tenth numb...
The average cost price of 25 pens (having equal cost price) decreased by Rs.4, when one of the pen is replaced by a new pen having cost price of Rs.60. ...
- David scored 144 runs in a match, and that made up 80% of the total team score. If 10 runs were added as extras, how many runs did the other players contri...
Komal bought 20 kg rice for Rs 30 per kg, b kg rice for Rs 35 per kg and (b + 4) kg rice for Rs 25 per kg. She mixed all type of rice together and the a...
The average weight of a group of five persons, A, B, C, D, and E is 60 kg. If another person K joins the group then the average weight of the group is d...
A park has an average of 140 visitors on Sundays and 80 on other day. The average number of visitors in a month of 30 days starting with Sunday is
The average expenditure of a man for the first five month is Rs.14000 and for the next seven months is Rs.12000. If he saves 17000 in that year then fin...
The average of a series of 30 numbers is 70. The difference between the largest number and the smallest number is 140. If the largest and the smallest n...
In a cricket match the captain of one of a team scored 26 runs more than the average runs scored by the remaining 6 batsmen of that team who batted in t...
The average age of a class of 22 girls is 18 years. If 2 new girls having average age of 12 years join the class, then the average age of the class beco...
Relevant for Exams:
