Q. 325.0( 1 Vote )
By examining the chest X - ray, probability that T.B is detected when a person is actually suffering is 0.99. The probability that the doctor diagnoses incorrectly that a person has T.B. on the basis of X - ray is 0.001. In a certain city 1 in 1000 persons suffers from T.B. A person is selected at random is diagnosed to have T.B. What is the chance that he actually has T.B.?
Answer :
Let us assume U1, U2 and A be the events as follows:
U1 = Person having T.B
U2 = Person not having T.B
A = Diagnosing T.B disease
From the problem:
⇒ 
⇒ 
⇒ P(A|U1) = P(diagnosing T.B disease for the person who actually having T.B)
⇒ P(A|U2) = P(diagnosing T.B disease for the person who don’t actually have T.B)
⇒ 
Now we find
P(U1|A) = P(The person has T.B and diagnosed T.B)
Using Baye’s theorem:
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
∴ The required probability is 
.
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PREVIOUSBag A contains 3 red and 5 black balls, white bag B contains 4 red and 4 black balls. Two balls are transferred at random from bag A to bag B and then a ball is drawn from bag B at random. If the ball drawn from bag B is found to be red, find the probability that two red balls were transferred from bag A to bag B.NEXTA test for detection of a particular disease is not fool proof. The test will correctly detect the disease 90% of the time, but will incorrectly detect the disease 1% of the time. For a large population of which an estimated 0.2% have the disease, a person is selected at random, given the test, and told that he has the disease. What are the chances that the person actually have the disease?
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