So close to completing this problem
Kenny, a computer games addiction counsellor for schools, claimed that his single test for addiction to game is 99% accurate. From previous data, it is estomated that 2% of the student's population suffered from computer games addiction.
(i) Show that the probability that a randomly chosen student is not a computer games addict and is diagnosed wrongly is 0.0098.
No problem with this.
(ii) Calculate the probability that a randomly chosen student will be diagnosed with addiction to computer games.
Ans: 0.0296
No issue here.
(iii) An external counsellor doubted Kenny's method and commented that about 33.1% of those diagnosed with game addiction using Kenny's test actually do not have any addiction. Verify the validity of this statement.
(i)/(ii)
(iv) To improve his method, Kenny will test those who are diagnosed as computer games addict a second time with 99% accuracy. Calculate the new probability that those diagnosed with game addiction actually do not have any addiction.
Ans: 0.00497
Stuck here argh.
Hi,
Part (iv) indeed requires some thought.
We are interested in P(non-addict | diagnosed with addiction twice).
So numerator is P(non-addict AND diagnosed with addiction twice)
= 0.98 (0.01) (0.01), whereby the diagnoses are wrongly classified as addiction.
Denominator is P(diagnosed with addiction twice)
= 0.02 (0.99) (0.99) + 0.98 (0.01) (0.01), whereby the diagnoses are either correct or wrong.
Thanks!
Cheers,
Wen Shih