A technology forecasting company needs to advise investors as to the probability that new designs of aircraft will become available. It analyses future scenarios as follows. With 80% efficient electrolysis (which is already available today), the probability of a hydrogen aircraft being economical in 5 years is 0.6. The efficiency of electrolysis can be improved to 90% within 5 years with a probability of 0.7. With 90% efficient electrolysis, the probability of a hydrogen aircraft being economical in 5 years is 0.8.

(a)Which of the probabilities in the above description is/are conditional?

(b)Draw a probability tree for the situation above (showing probabilities of electrolysis efficiency and an economical hydrogen aircraft in 5 years). (c)What is the probability that an economical hydrogen aircraft will be developed in 5 years? If an economical hydrogen aircraft is developed in 5 years, research into electric aircraft will be cut back so that the probability of an economical electric aircraft being developed in 7 years is 0.5. If an economical hydrogen aircraft is not developed in 5 years, the probability of an economical electric aircraft being developed in 7 years is 0.9.

(d)Extend the probability tree from (b) to also include probabilities of an economical electric aircraft in 7 years.

(e)What is the probability that an economical electric aircraft will be developed in 7 years?