The requirement is to determine what the probability of frost must be for Ball to be indifferent to spending $20,000 for frost protection. In other words, you must find the point at which the cost of the frost protection equals the expected value of the loss from frost damage. The table below summarizes the possible outcomes.
The difference between the market value of protected and unprotected strawberries if a frost were to occur is $100,000. Since we want to determine the probability of a frost when the expected value of the loss from frost damage is $20,000, this probability can be calculated as follows:
| Frost | Frost-free | |
| Protected |
$180,000
Market value
| $1200,000 Market value |
| Unprotected | $80,000 Market value | $120,000 Market value |
The difference between the market value of protected and unprotected strawberries if a frost were to occur is $100,000. Since we want to determine the probability of a frost when the expected value of the loss from frost damage is $20,000, this probability can be calculated as follows:
Loss from
damage
| × | Probability of frost | = | Expected value of the loss |
| $100,000 | × | P | = |
$20,000
$20,000
|
| P | = | $100,000 | ||
| P | = | .200 |
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