60% chanceLoss of 80 $40% chanceNo loss, no win I am willing to pay at most                                              $ to avoid the lottery.

The question seems to be asking for the expected value of the lottery, which is the maximum amount you should be willing to pay to avoid it.

Here's how to calculate it:

1. First, calculate the expected loss from the 60% chance of losing $80. This is done by multiplying the probability of the event (60$80). So, 0.6 * 80 = $48.

2. Then, calculate the expected gain from the 40% chance of neither losing nor winning. This is done by multiplying the probability of the event (40% or 0.4) by the amount of the gain ($0, since there's no loss or win). So, 0.4 * 0 =$0.

3. Add the expected loss and the expected gain to get the expected value of the lottery. So, 48 + 0 = $48.

Therefore, you should be willing to pay at most $48 to avoid the lottery.