Level of question:Secondary
Question:
A rare disease infected 1 in 1000 people in the population. A test for the disease is accurate 99% of the time when given to an infected person and also when given to a heathy person.
 Fill out a twotier tree diagram and find the probability of the false positive(i.e the conditional probabily of being healty even when tested postive by the test) Comment on the result?
 John after tested once positive was tested again .Fill out completely a three tier diagram and find the probabilty of false doublepositive(ie. the conditional probabily of healthy even john was tested positive twice) what is the probability of a person being healthy and twicepositively tested?
Thankyou for your kindy help!!
Yours sincerely
James
Hi James,
I used the letter I to designate infected, H to designate healthy, P to designate a positive test and N to designate a negative test. The twotier tree diagram is then
The probability of a false positive is the conditional probabily of being healty even when tested postive by the test, that is Pr(HP). Thus to find the probability of a false positive you need to calculate:
Pr(HP) = Pr(H and P)/Pr(P)
From the tree diagram
Pr(H and P) = (999/1000) 0.01 = 0.00999.
You can receive a positive test by either being healthy and receiving a positive test or being infected and receiving a positive test. Thus:
Pr(P) = (999/1000) 0.01 + (1/1000) 0.99 = 0.01098
Hence the probability of a false positive is:
Pr(HP) = Pr(H and P)/Pr(P) = 0.00999/0.01098 = 0.9098
Now put a third tier on the tree diagram to answer part 2.
Cheers,
Penny
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