0.4% of the devices have a bug that makes them short circuit afte 10hours of us.. The director picked a quick test for the defect -- however, it misses the defect 3% of the time. She wants to know the chance that a device has this defect after testing positively for it.

She was told that if she also knows ........................

(a) The joint probability of a device being defective and short circuiting

(b) tests false positive rate

you can use the ..................

(a) multiplication rule (b) Bayes rule

-------------?------------- to help her out..

(a) Law of total probability P(A|B) = P(B|A) P(A) / [P(B|A)P(A) + P(B|Ac)P(Ac)

(b) Original version P(A|B| = P(B|A) P(A)/P(B)