A test indicates the presence of a particular disease 90% of the time when the disease is present and the presence of the disease 2% of the time when the disease is not present. If 0.5% of the population has the disease, calculate the conditional probability that a person selected at random has the disease if the test indicates the presence of the disease.
A hospital receives two-ﬁfths of its ﬂu vaccine from Company A and the remainder from Company B. Each shipment contains a large number of vials of vaccine. From Company A, 3% of the vials are ineffective; from Company B, 2% are ineffective. A hospital tests n = 25 randomly selected vials from one shipment and ﬁnds that 2 are ineffective. What is the conditional probability that this shipment came from Company A?
The solution provides the brief method for the calculation of probability using Bayes theorem. Formula for the calculation and Interpretations of the results are also included.