What is the expected value if a precautionary treatment is applied for a 20% chance of a major insect infestation that reduces per acre profits by $60?

To calculate the expected value of applying a precautionary treatment for the insect infestation, we start by assessing the potential financial impact. The situation states there is a 20% chance of a major insect infestation, which would incur a loss of $60 per acre.

The expected value is computed using the probability of the event occurring multiplied by the negative profit impact, added to the probability of the event not occurring multiplied by a gain (or no loss). In this case, since we are focusing on the loss from the infestation, we can summarize it as follows:

1. The chance of the infestation occurring is 20% (or 0.20), leading to a loss of $60. Therefore, the expected loss from the infestation is:

( \text{Expected loss} = 0.2 \times (-60) = -12 )

2. The chance of the infestation not occurring is 80% (or 0.80), which means that there would be no loss, resulting in:

( \text{Expected gain} = 0.8 \times 0 = 0 )

Now, adding these two expected values gives us the total expected value:

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-12 + 0 = -12