One local hospital has just enough space and funds presently available to start either a cancer or heart research lab.If administration decides on the cancer lab,there is a 20 percent chance of getting $100,000 in outside funding from the American Cancer Society next year,and an 80 percent chance of getting nothing.If the cancer research lab is funded the first year,no additional outside funding will be available the second year.However,if it is not funded the first year,then management estimates the chances are 50 percent it will get $100,000 the following year,and 50 percent that it will get nothing again.If,however,the hospital's management decides to go with the heart lab,then there's a 50 percent chance of getting $50,000 in outside funding from the American Heart Association the first year,and a 50 percent chance of getting nothing.If the heart lab is funded the first year,management estimates a 40 percent chance of getting another $50,000,and a 60 percent chance of getting nothing additional the second year.If it is not funded the first year,then management estimates a 60 percent chance for getting $50,000,and a 40 percent chance of getting nothing in the following year.For both the cancer and heart research labs,no further possible funding is anticipated beyond the first two years.What is the expected value for the optimum decision alternative?
A)$100,000
B)$60,000
C)$50,000
D)$40,000
E)$20,000

Question

Quizplus · Accepted Answer

To calculate the expected value for each decision alternative, we must first calculate the expected value for each possible outcome and its probability of occurring.

For the cancer lab:
Probability of getting $100,000 in outside funding = 0.20
Probability of getting nothing = 0.80
Expected value for first year = (0.20 * $100,000) + (0.80 * $0) = $20,000

If the cancer lab is not funded in the first year:
Probability of getting $100,000 in outside funding in the second year = 0.50
Probability of getting nothing in the second year = 0.50
Expected value for second year = (0.50 * $100,000) + (0.50 * $0) = $50,000
Expected value for two years = $20,000 + $50,000 = $70,000

For the heart lab:
Probability of getting $50,000 in outside funding in the first year = 0.50
Probability of getting nothing = 0.50
Expected value for first year = (0.50 * $50,000) + (0.50 * $0) = $25,000

If the heart lab is funded in the first year:
Probability of getting $50,000 in outside funding in the second year = 0.40
Probability of getting nothing in the second year = 0.60
Expected value for second year = (0.40 * $50,000) + (0.60 * $0) = $20,000
Expected value for two years = $25,000 + $20,000 = $45,000

If the heart lab is not funded in the first year:
Probability of getting $50,000 in outside funding in the second year = 0.60
Probability of getting nothing in the second year = 0.40
Expected value for second year = (0.60 * $50,000) + (0.40 * $0) = $30,000
Expected value for two years = $25,000 + $30,000 = $55,000

Therefore, the expected value for the cancer lab is $70,000 and the expected value for the heart lab is $45,000 if it is funded the first year and $55,000 if it is not funded the first year. Therefore, the best choice is to start the heart research lab.

One Local Hospital Has Just Enough Space and Funds Presently