Chicken Little is risk-neutral, but is concerned about the sky falling. She believes that there is a 25% chance of this happening. If it does, her egg collection (valued at $2,000,000) will be crushed. A backyard bunker salesman offers to sell her a disaster shelter, installed, for only $400,000. Given Chicken Little’s beliefs, should she buy the shelter?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Chicken Little is risk-neutral, but is concerned about the sky falling. She believes that there is a 25% chance of this happening. If it does, her egg collection (valued at $2,000,000) will be crushed. A backyard bunker salesman offers to sell her a disaster shelter, installed, for only $400,000. Given Chicken Little’s beliefs, should she buy the shelter?

Expert Solution
Step 1

For a discrete random variable, X, with probability distribution P(X) , the expected value of X can be given as, EX=X·PX.

Assume, X be the random variable representing the loss (in dollars). Therefore, if sky falling happens then X=2000000 and if sky falling does not happen then X=0.

If the expected loss for the woman is greater than $400000, then she should buy the shelter, otherwise there is no need of buying the shelter. 

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