Clinical testing of chemical compounds for approval as drugs goes through three successive stages. A compound that fails in one phase does not proceed to subsequent phases.

i) Phase 1: testing on about 50 healthy individuals to investigate possible side effects; 70% of compounds pass Phase 1 testing and proceed to Phase 2.

ii) Phase 2: testing on about 200 patients to investigate effectiveness in curing illness; 43% of compounds pass Phase 2 testing and proceed to Phase 3.

iii) Phase 3: testing on about 3000 patients to investigate effectiveness in curing illness; 67% of compounds pass Phase 3 testing and are approved for clinical use.

a) Draw a probability tree to represent this situation.

b) What method of probability assessment is used to estimate the probabilities in your tree?

c) Which probabilities are conditional?

d) What is the probability of a chemical compound passing all three phases of testing and becoming approved for clinical use?