hello everyone. Recently my maths teacher gave me a probability question because im finding the yr 12 curriculum pretty easy but im having trouble completing this question. just wondering if any smart people would be able to complete the question so i can see how its done.

Much appreciated.

QUESTIONS

A group of five dentists is considering the construction of a private clinic. If the demand is high (favourable market for the clinic), the dentists could realise a net profit of $100000. If the market is not favourable, there will be a loss of $40000. Of course they don’t have to proceed at all.

a. In the absence of any market data, the best the dentists can guess is that there is a 50-50 chance the clinic will be successful. Construct a decision tree to help analyse this problem and conclude what should the dentists do?

b. The dentists approach a market research firm that offers to perform a study of the market at a fee of $5000. The market research company claims its experience enables it to make the following statements

Probability of a favourable market given a favourable study: 0.85

Probability of a unfavourable market given a favourable study: 0.15

Probability of a favourable market given a unfavourable study: 0.12

Probability of a unfavourable market given an unfavourable study: 0.88

Probability of a favourable research study: 0.55

Probability of a unfavourable research study:0.45

Develop a new decision tree to reflect the available options with the market

study and recommend what the dentists should do.

c. What is the maximum amount that the dentists can pay to the market research firm?