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One Local Hospital Has Just Enough Space and Funds Currently

question 91

Multiple Choice

One local hospital has just enough space and funds currently 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 is 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 for 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 probability that the heart lab will be funded in both the first and second years?

Definitions:

Performance

The accomplishment of a task or duty in accordance with a contract, including the delivery of goods or services.

Full Satisfaction

The complete fulfillment or settlement of a debt, obligation, or another requirement.

Possession

The physical holding or control of an object or property, which may or may not be accompanied by legal ownership.

Debt

An amount of money borrowed by one party from another, typically with the obligation to pay back with interest.