A proposed shopping center will provide strong competition for downtown businesses like L. S. Clothiers. If the shopping center is built, the owner of L. S. Clothiers feels it would be best to relocate.
The shopping center cannot be built unless a zoning change is approved by the town council. The planning board must first make a recommendation, for or against the zoning change, to the council.
Let:
A1 = town council approves the zoning change
A2 = town council disapproves the change
Prior Probabilities
Using subjective judgment: P(A1) = .7, P(A2) = .9
New Information
The planning board has recommended against the zoning change. Let B denote the event of a negative recommendation by the planning board.
Given that B has occurred, should L. S. Clothiers revise the probabilities that the town council will approve or disapprove the zoning change?
Conditional Probabilities
Past history with the planning board and the town council indicates the following:
P(B|A1) = .2 P(B|A2) = .9