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238 Revising judgments in the light of new information
million units is 0.4. Revise the sales manager’s estimate in the light
of the sales forecast.
(3) The probability of a machine being accidentally overfilled on a given
day is 0.05. If the machine is overfilled there is a 0.8 probability that
it will break down during the course of the day. If the machine is
not overfilled the probability of a breakdown during the day is only
0.1. Yesterday the machine broke down. What is the probability
that it had been accidentally overfilled?
(4) A mining company is carrying out a survey in a region of Western
Australia. On the basis of preliminary results, the company’s senior
geologist estimates that there is a 60% probability that a particular
mineral will be found in quantities that would justify commercial
investment in the region. Further research is then carried out and
this suggests that commercially viable quantities of the mineral
will be found. It is estimated that this research has a 75% chance
of giving a correct indication. Revise the senior geologist’s prior
probability in the light of the research results.
(5) A company which manufactures compact discs has found that
demand for its product has been increasing rapidly over the last
12 months. A decision now has to be made as to how production
capacity can be expanded to meet this demand. Three alternatives
are available:
(i) Expand the existing plant;
(ii) Build a new plant in an industrial development area;
(iii) Subcontract the extra work to another manufacturer.
The returns which would be generated by each alternative over the
next 5 years have been estimated using three possible scenarios:
(i) Demand rising at a faster rate than the current rate;
(ii) Demand continuing to rise at the current rate;
(iii) Demand increasing at a slower rate or falling.
These estimated returns, which are expressed in terms of net present
value, are shown below (net present values in $000s):
Course of
action
Demand rising
faster
Scenario
Demand rising
at current rate
Demand increasing
slowly or is falling
Expand 500 400 −150
Build new plant 700 200 −300
Subcontract 200 150 −50