A fictional company (let’s call it Curie-Franklin-Meitner-Mirzakhani-Noether-Rubin, or CFMMNR) has branched out from its other work on building and launching fictional telescopes (where it bought out the fictional FWO operation) and visiting web sites (it has browsed and looked at https://www.ias.ac.in/womeninscience and other sites), and is now apparently involved in mining. We are pleased to say that this company, CFMMNR, is responsible and cares about the environment and the welfare of its workers and employees. CFMMNR has several options for a mining project.
It starts out with $13,000.
There is a probability of 50% = 0.5 = 1/2 that precious material A is underground and that it would be worth $20,000. There is a probability of 50% = 0.5 = 1/2 that nothing useful is underground and that it would be worth $0.
Option 1 is to do nothing and keep the money we started with.
Option 2 is to spend $10,000 and mine for A.
CFMMNR has the option of spending $1,000 on a consultant. When the consultant (call her Rosalind) says that material A is present, she has a probability of 0.7 of being correct and 0.3 of being incorrect. When the consultant says that mineral A is not present, then she has a probability of 1/30 of being incorrect and a probability of 29/30 of being correct.
When we do the mathematics, it follows that there would be a probability of 0.7 that she would say that material A is present.
Option 3 is to spend $1,000 and hire the consultant, and then to make a decision (to follow through with mining or instead doing nothing further) based on the consultant’s recommendation.
1a (20 marks)
Using Netica, set up a decision network for a choice between Option 1, Option 2 and Option 3.
(At this stage, do not include Option 4.)
In your answer, give any prior probabilities, any conditional probability tables (CPTs), any utility functions, explain your working and show your choice out of option 1, option 2 and option 3.
State how much money you expect CFMMNR to have.
Moving on from Qu 1a and leading now into Qu 1b, Option 4 is instead to mine for precious material B (and then see what happens afterwards). Doing this would cost $2,000.
If we do mine for B, then with probability 3/5 = 0.6 = 60% we would find $1,000 worth of B and then stop.
But with probability 2/5 = 40% = 0.4, we would find
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