Answer:
We can think in this situation as:
There is 10% (or a probability equal to 0.1) where the citrus grower's profit will be reduced by $15,000
There is 10% (or a probability equal to 0.1) where the citrus grower's profit will be reduced by $25,000
And in the remaining 80% (or a probability equal to 0.8), the profit does not change.
Then the expected value for the total profit can be written as:
EV = $100,000 + ( 0.1*(-$15,000) + 0.1*(-$25,000) + 0.8*$0)
= $96,000
In the case where the citrus grower spends $5000 to protect the fruits against possible bad weather, there is a 100% that is profit will not change, but he must pay $5,000
Then his profit will be:
P = $100,000 - $5,000 = $95,000
So in this case, the profit is $1000 less than the expected profit in the prior case. So the scenario where he does not buy the protection has a larger expected profit, which may mean that is better to not buy it (in a straight mathematical point of view)
One also could think that the values are really close together, so buying the protection does not mean a big change, and increases the security
