There is a rare disease, probability of someone getting the disease is P(D) = 0.0001. If you have the disease, it will kill you ( P(K|D) = 1 ).

a. There is a test for that disease but it is not always correct means if you have the disease, the test will be positive in 95% of the times ( P(T|D) = 0.95)) and negative in 5% of the times ( P(~T|D) = 0.05).

Also if you do not have the disease, the test might comes positive : P(T|~D) = 0.01 so we can say P(~T|~D) = 0.99

Now you took the test and it came back positive, what is the probability that you actually have the disease? (P(D|T) = ?)

what this value says about the reliability of the test?

b. There is a cure for this disease (we show it by c) but the cure itself might kill you means if you have the disease or not, if you use the cure, it will kill you with the probability of 5% ( means P(K|C,D) = P(K|C,~D) = 0.05) so P(~K|C,D) = 0.95).

so if the test came back positive, should you get the cure? hint : you need to compare these two values P(K|T,~C) vs P(K|T,C) then explain your decision)