3% of the population has disease X. A laboratory blood test has (a) 96% effective at detecting dis

bacfrancaiso0j 2022-04-30 Answered
3% of the population has disease X.
A laboratory blood test has
(a) 96% effective at detecting disease X, given that the person actually has it.
(b) 1% “false positive” rate. i.e, a person who does not have disease X has a probability of 0.01 of obtaining a test result implying they have the disease.
What is the probability a person has the disease given that the test result is positive?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Genesis Reilly
Answered 2022-05-01 Author has 12 answers
A "False positive" means just what it sounds like: the test gives a positive result and this is wrong (ie: the patient does not actually have the disease). The false positive rate is the probability of a positive result for patients without the disease.
So let D be the event of having the disease, and T be the event of the test being positive.
"3% of the population has disease X."
P ( D ) = 0.03
"A laboratory blood test has (a) 96% effective at detecting disease X, given that the person actually has it."
P ( T D ) = 0.96
"A laboratory blood test has (b) 1% “false positive” rate. i.e, a person who does not have disease X has a probability of 0.01 of obtaining a test result implying they have the disease."
P ( T D ) = 0.01
"What is the probability a person has the disease given that the test result is positive?"
Now find P ( D T ) using what you know of conditional probability (hint: Bayes' Rule) and the Law of Total Probability.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2022-05-26
Consider the generator polynomial 100101 and the data 1011100110001. Applying the CRC algorithm we get the transmitted message:
1011100110001 D a t a 00011 R e m a i n d e r
I need to make 3 errors in the transmitted word (that is, bit flips) that the receiver won't notice. Hence, the CRC algorithm will fail to notice the errors and will falsely the data. How can this be arranged?
asked 2022-05-09
Descartes rule of sign can be used to isolate the intervals containing the real roots of a real polynomial. The rule bounds the number of roots from above, that is, it is exact only for intervals having zero or one root. In methods like VCA, VAS and similar, it is used to count the number of sign changes to determine the number of roots.
My question is, what to do if the rule reports, say, two sign changes for interval which does not contain any roots?
asked 2022-04-06
What is the rationale behind ROC curves?
I am not sure how ROC curves work. I see that the X-Axis is the false positive rate while the Y axis is the true positive rate.
1) I don't understand how for a given statistical learning model, you could have the true positive and false positive rate to vary from 0 to
1. Are you changing parameters in the model to make it so?
2) What about true negatives and false negatives? How are these represented in the curve?
asked 2022-06-08
if 1:1000 of people is sick. the probability to be false positive is 0.07. if a person is sick there is not chance the test for the disease is wrong. If someone random is got a positive result, what are the chances he's actually sick?
I got 1.5% and wanted to check because I feel it should be more since the diagnose is never wrong. I took 1/1000 and divided it by 0.07+1/1000 and multiplied by 100 to get the percent.
asked 2022-06-01
According to my research the Fowlkes-Mallows Index should be a good tool to get a comparable evaluation score, but I am not sure about the correct application.
Currently I calculate the true positives, false positives and false negatives for each cluster, then sum them together for total values and add them in the formula.
F M = T P T P + F P T P T P + F N
where T P is the number of true positives, F P is the number of false positives, and F N is the number of false negatives.
Is this the correct application of the Algorithm?
asked 2022-05-07
How the false positive value affects accuracy?
T P   ( t r u e   p o s i t i v e )   =   2739
T N   ( t r u e   n e g a t i v e )   =   103217
F P   ( f a l s e   p o s i t i v e )   =   43423
F N   ( f a l s e   n e g a t i v e )   =   5022
a c c u r a c y = T P + T N T P + T N + F P + F N
In this case the accuracy is 0.68. Can I say that I have low accuracy because the value false positive is high? There is any relathion between false positive and the parameters true positive or true negative?
asked 2022-06-05
While it makes some sense, it's not clear to me why those are different. If a test, say medical test, is correct 90% of time then chances of it being wrong is 10%.
But I've read things that say in medical field test with high accuracy for negatives are used as screening method and more expensive tests which are high accuracy positive tests are used only when former tests come positive. Because if former came negative we are confident patient doesn't have a disease but if it comes positive we are not as sure, thus we do expensive test. Which of course, makes sense.
I get there are 4 events:
1. Test is +, patient has a disease
2. Test is -, patient doesn't have a disease
3. Test is +, patient doesn't have a disease
4. Test is -, patient has a disease