Question

A shopping center project is proposed to the city council. It cannot be built unless a zoning change is approved by the council. The planning board must first make a recommendation, for or against the zoning change, to the council.
Let A1 = city council approves the zoning change A2 = city council disapproves the change

The prior is: Pr(A1) = .7,   Pr(A2) = .3

Let B denote the event of a negative recommendation by the planning board.

Past history with the planning board and the city council indicates the following

Pr(B|A1) = .2, Pr(B|A2) = .9

3. ____ The planning board has recommended against the zoning change. What is the posterior probability that the city council will approve the zoning change? a) 0.2 b) 0.22 c) 0.3 d) 0.34 e) 0.43


4. ____ You own a local store in the downtown of the city. If the shopping center project is not allowed, your revenue will be $3,000. If allowed, your revenue will be $1,000. The cost of operation is $2,000. Then, you will choose to ______ because your expected profit (or loss if you choose to exit) is ____.

a) Stay, $140 b) Stay, $320 c) Stay, $400 d) Exit, $140 e) Exit, $320

Answer 1

Given Information

• We are find
  
  
  
  
  
  
  
  
• The approval of the council is the final decision.
  Let the Y denote the revenue earned by the local store.
  The random variable is given by:
  
  That is,
  
  
  The cost of operation is $2000
  
  let Z be the random variable denoting profit of the local store.
  Clearly,
  
  Now,
  
  
  
  
  
  
  
  
  Hence, there is an expected profit of $400 and hence, the local store should be built.
  
  

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