Compute P(S|F), P(N|F), P(S|U), P(N|U) as well as P(F) and P(U) A major use of decision tree

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Compute P(S|F), P(N|F), P(S|U), P(N|U) as well as P(F) and P(U)

A major use of decision tree analysis is to estimate the expected value of information. We will use the following simple example to illustrate the application process.

In this case, a CEO needs to decide whether to invest $5 million to improve an existing product, which is sure to yield a profit of $7 million, or to develop a new product, which will yield a profit of $15 million if successful or $0 if not successful. A consultant offers to conduct a market forecast for the new product for a fee of $0.5 million. Should the CEO hire the consultant and in which product should the CEO invest?

A 2-stage tree shown below describes the decision process: the first stage is to decide whether to acquire the information; the second stage is to decide which product to invest. For simplicity, we assume that the CEO is risk-neutral and wants to maximize the expected net profit.