Question

18
4
By examining the Covid-19 test report of some laboratory, the
probability that a person is diagnosed Covid-19 positive when he is
actually suffering from it is 0.99. The probability that the report
incorrectly diagnosed a person to be Covid-19 positive on the basis of
report is 0.001. In a certain city 300 of 1000 persons suffer from Covid-
19.
Based on the above information answer the following.
1.
The conditional probability that a person is diagnosed Covid-
19 positive given that he actually has Covid-19

a) 0.7
b) 0.99
c) 0.001
d) 0.3

2.
A person is selected at random and is diagnosed with Covid-
19. What is the chance that he actually has Covid-19
a) 0.99
b) 0.91
c) 297/304
d) 304/297

3.
MCD wants to keep a check, so an officer during checking
selects the report randomly. According to the report, person
is diagnosed Covid-19 positive. What is the probability that
the person doesn't have actually Covid-19.
a) 0.001
b) 7/297
c) 7/2977
d) 0.99

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Answer 1

Step-by-step explanation:

By examining the chest X-ray, the probability that a person is diagonased with TB when he is actually suffering from it, is 0.99. The probability that the doctor incorrectly diagnoses a person to be having TB, on the basis of X-ray reports is 0.001. In a certain city , 1 in 1000 persons suffers from TB. A person is selected at random and is diagoanl to have TB. What is the chance that he actually has TB?

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Solution

Let E= event that the doctor diagonoses TB, <br>

=event that the person selected is suffering from TB, and <br>

=event that the person selected is not suffering from TB. <br> Then ,

. <br>

= probability that TB is diagnosed, when the person actually has TB <br>

<br>

= probability that TB is diagnosed, when the person has no TB <br>

<br> Using Bayes's theorem, we have <br>

= probability of a person actually having TB, if it is knows that he is diagonal to have TB <br>

<br>

. <br> Hence, the required probability is