Problem: A manufacturer must decide whether to build a small or a large plant at a new location. The production manager believes that the demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. However, the manager can conduct a test to see if there is a popular local competitor in the new location or not. The probability of a popular competitor is estimated to be 0.3, and the manager believes that if there is such a competitor the probability of high demand is 0.1, and in the absence of a popular competitor the probability of high demand is 0.8.
If a small plant is built, and demand is high, the value of the profit will be 300,000. If a small facility is built and demand is low, the value of the profits is $200,000. However, if the large plant is built and the demand happens to be high, the value of the profits is $500,000. But, if a large facility is built and the demand turns out to be low, the profit is $100,000.
What is the prior probability that the demand is high?
a 0.6
b 0.4
c 0.1
d 0.8