16. Datasyitis is a strange disease with no obvious symptoms that randomly develops in 1 in 1000 people

across the world. Fisher Rx has recently developed a highly accurate diagnostic test that correctly

identifies 99% of all positive cases (in other words, sensitivity = 99% ), and correctly identifies all

unaffected individuals (in other words, specificity = 100% ). Let T denote the test result and D the

disease state for a given individual.

a) [1 point] What is the probability that you have datasyitis, that is P(D+) ?

b) [3 points] What is the probability that you will develop datasyitis and test positive, that is P(T+D+) ?

c) [3 points] Using the law of total probability, what is the chance that you will test positive for datasyitis,

that is P(T+) ?

d) [4 points] Suppose that you have tested positive for datasyitis. What is the probability that you have

datasyitis, that is P(D+|T+) ? Your doctor tells you that this means that you have a 99% chance of

developing datasyitis, as this