OCR S4 2014 June — Question 2

Exam BoardOCR
ModuleS4 (Statistics 4)
Year2014
SessionJune
TopicConditional Probability
TypeStandard two-outcome diagnostic test

2 During an outbreak of a disease, it is known that \(68 \%\) of people do not have the disease. Of people with the disease, \(96 \%\) react positively to a test for diagnosing it, as do \(m \%\) of people who do not have the disease.
  1. In the case \(m = 8\), find the probability that a randomly chosen person has the disease, given that the person reacts positively to the test.
  2. What value of \(m\) would be required for the answer to part (i) to be 0.95 ?