Answer:
a) 0.04
b) The choice of renting a protected area should be made
c) Indifference probability, P = 0.25
Step-by-step explanation:
a) Probability that the 25-year flood takes place in a given year.
This means that the flood is taking place once in 25 years, and the probability that it takes place in this given year is 1/25 = 0.04
b) The contractor is left with two alternatives, either to stay in protected area or flood plain area.
We will calculate the cost of staying in protected area and the loss incurred if he stays in the flood plain area. The one with the lesser value will be the more preferred decision.
Probability of a damaging flood, pr (flood) = 0.02
Probability of high damage if he chooses the flood plain = 0.5
Pr(high damage) = 0.02 * 0.5 = 0.01
Probability of low damage if he chooses the flood plain = 0.5
Pr(low damage) = 0.02 * 0.5 = 0.01
Loss(low damage) = $400,000
Loss(High damage) = %600,000
Average loss = [Pr(low damage)*Loss(low damage)] + [Pr(high damage) *Loss(High damage) ]
Average loss = (400000*0.01) + (600000*0.1)
Average loss = 4000 + 6000
Average loss = $10,000
Winter lasts for three months, i.e number of months = 3
Therefore the costs of renting the areas should be charged per month
Cost of renting flood plain = $10000 per year = 10000/12 = $833.22/month
Cost of renting protected area = $35000 per month = 35000/12 = $2916.67/month
The protected area is not used
Cost of rent for 1 month = $2916.67 - $833.22
Cost of rent for 1 month = $2083.45
Cost of renting protected area in 3 months = 3 * 2083.45 = $6250.34
Since the cost of renting protected area is less than the loss incurred in flood plain area, the contractor should rent a protected area
c)The principle of indifference states that in the absence of any relevant evidence, agents should distribute their credence equally among all the possible outcomes under consideration.
The probability of high or low damage = 0.50
Since there are just two options, and indifference does not assign probabilities based on prior information
Probability(flood) = 0.5
Probability that a flood with high damage will occur = Probability (flood) * Pr(high damage) = 0.5 * 0.5 = 0.25
Probability that a flood with low damage will occur = Probability (flood) * Pr(low damage) = 0.5 * 0.5 = 0.25
