probabilty

Question

One in two hundred people in a population have a particular disease. A
diagnosis test gives a false positive 3% of the time, and a false negative
2% of the time. Ross takes the test and the report comes positive. Find the
probability that Ross has the disease.

Comments

is answer 0.247.?

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havent solved yet,

can you elaborate your ans

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check in asnwer i have explained..:)

Answer 1

P(person having disease)=1/200

P(person having no disease)=199/200

P(person having no disease and test has come +ve(false +ve)) ----this is probability of person having no disease but test has come positive

As in given qsn 3% of time test come as false positive,so probability is=3/100*199/200

P(person having disease and test has come -ve(false neagtive)) this is probability of person having disease but test has come neagtive,so as mentioned in qsn 2% of time this can happen= 2/100*199/200

So it means for 98% time you get test as +ve correctly its becz

As said for 2% of time false -ve test can come

P(person having disease and test has come +ve)=98/100*1/200

Now as asked in qsn ross takes test and his report comes +ve,we need to find probability of ross having disease given that test has come +ve.

P(person having disease/test has come +ve)=(98/100)*(1/200) / [ ( 98/100)* (1/200) +(3/100)*(199/200)]=0.247