# Find the value of p based on expected returns

2. If p is the probability of Event 1 and (1-p) is the probability of Event 2, based on the expected returns, for what values of p would you choose A? B? C? Values in the table are payoffs.

Choice/Event Event 1 Event 2

A 0 20

B 4 16

C 8 0

(Here are some hints for solving this question, since it's somewhat

challenging:

o first derive the expected returns, as a function of p, for each of the

three choices, A, B, C.

o then compare the expected returns in pairs to see for what ranges of p:

(1) A's return exceeds B's and vice versa

(2) A's return exceeds C's and vice versa

(3) B's return exceeds C's and vice versa

This should give you enough information to answer the question.

It might also help to graph each return function against p. Remember that since p is a probability, it can only take on values between 0 and 1.)

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Choice Event 1 Event 2 Expected ...

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The expert finds the value of p based on expected returns.