Question

Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish.

Guide to marks: 20 marks - 4 for (a), 2 for (b), 6 for (c), 2 for (d), 6 for (e)

Round probability calculations to 2 decimal places.

A firm is considering marketing a new product which will be a success or a failure. The prior probability of success is judged to be 0.3.

If the product is marketed and is a success the firm expects to earn $1,000,000, while a failure is expected to lead to a loss of $600,000.

(a) Should the product be marketed? Why?
(b) What is the expected value of perfect information about the success or failure of the product?

The firm is considering a market survey whose results can be classified as favourable or unfavourable. Given past experience with the market survey personnel, the conditional probabilities are p(favourable|success) = 0.7 and p(unfavourable|failure) = 0.8.

(c) Revise the prior probabilities in light of these likely survey results.
(d) What is the posterior probability of success given a favourable survey result?
(e) What is the maximum the firm should pay for the market survey?

Answer 1

Probability of success =0.3

Probability of failure

Expected earning = 1000000*0.3 - 600000*0.7 = 300000-420000 = -120000

Hence the product shoud not be slated.

b) Expected value = -120000

p(f/s) =0.7 and p(u/F) = 0.8 taking the assumption p(f) =0.5 and p(u) =0.5, p(s) =0.3 and p(F)=0.7

p(s/f) = p(f/s) * p(s)/p(f) = 0.7*0.3 / 0.5 = 0.105

p(s/u) = p(u/s)* p(s)/ p(u) = 0.3*0.3/0.5 = 0.045

Similarly for p(F/f) and p(F/u) will sum upto = 0.8 { use the formula above}

Posterior probability of success given favourable survey results is P(s/f) = 0.105