# Bayes' Theorem - Sample Question

1.6-12.

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.

1.6-13.

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?

https://brainmass.com/statistics/bayesian-probability/bayes-theorem-sample-question-252171

#### Solution Summary

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.