Question

Researchers for the University of Maryland Department of Civil and Environmental Engineering used stochastic dynamic programming to determine optimal load estimates for electric power (Journal of Energy Engineering, Apr. 2004). One objective was to determine the probability that a supplier of electric power would reach or exceed a specific net profit goal for varied load estimates. All load estimates in the study yielded a probability of .90. Consider two different suppliers of electric power (Supplier A and Supplier B) acting independently.

a. What is the probability that both suppliers reach their net profit goal?

b. What is the probability that either Supplier A or Supplier B reaches its net profit goal?

Answer 1

probability for exceed specific net profit goal, p =0.9

a)

the probability that both suppliers reach their net profit goal =1st one exceed specific net profit goal *2nd exceed specific net profit goal = p*p = 0.9*0.9 = 0.81

the probability that both suppliers reach their net profit goal is 0.81

b)

probability that either Supplier A or Supplier B reaches its net profit goal = 1st one exceed specific net profit goal *2nd not exceed specific net profit goal+ 1st one not exceed specific net profit goal *2nd exceed specific net profit goal

probability that either Supplier A or Supplier B reaches its net profit goal = p*(1-p) + (1-p)*p

probability that either Supplier A or Supplier B reaches its net profit goal = 0.9*(1-0.9)+(1-0.9)*0.9

probability that either Supplier A or Supplier B reaches its net profit goal =0.09+0.09

probability that either Supplier A or Supplier B reaches its net profit goal = 0.18

probability that either Supplier A or Supplier B reaches its net profit goal is 0.18