Random Drug testing Question

Q)

Random drug testing is to be carried out at the Beijing Summer Olympics in 2008. It is known that the drug test for Human Growth Hormone (HGH) possesses the following properties: If an athlete has taken HGH the test will be positive with probability 0.95. If an athlete has not taken HGH the test will be negative with probability 0.98. At the Athens Olympics it was estimated that 0.5 of one percent of all athletes took HGH.

(a) Represent the above situation on a Venn diagram. Carefully define the sample

space when doing so.

(b) What is the probability that an athlete who is randomly tested for HGH at Beijing

has not taken HGH, given their test is positive?

(c) What is the probability that an athlete who is randomly tested for HGH at Beijing

has taken HGH, given their test is negative?