Question 1162491
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If *[tex \Large p] is the probability of good weather, you make *[tex \Large 1.5p] million if you build the greenhouse and *[tex \Large 2.0p] million if you don't, so the expected value if there is good weather is *[tex \Large 3.5p] million.


If *[tex \Large p] is the probability of good weather, then *[tex \Large 1\,-\,p] is the probability of bad weather since so-so weather and its effects are not considered in this problem.  If there is bad weather, you make *[tex \Large 1.0(1\,-\,p)] million if you don't build the greenhouse and *[tex \Large 2.5(1\,-\,p)] million if you do, so the expected value if there is bad weather is *[tex \Large 3.5(1\,-\,p)] million.


For indifference, the two expected values must be the same, hence


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ p\ =\ 1\ -\ p]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ p\ =\ \frac{1}{2}]
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
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