Suppose that the weather forecast indicates a 10% chance that cold weather will reduce the citrus grower’s profit from $100,000 to $85,000 and a 10% chance that cold weather will reduce the profit to $75,000. Should the grower spend $5000 to protect the citrus fruit against the possible bad weather?

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

yes

step-by-step explanation:

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional