10% ChanceWin 0 $90% ChanceWin 100 $ I am willing to pay at most                                              $ to play the lottery.

The expected value of the lottery can be calculated using the formula:

Expected Value = (Probability of Winning * Amount Won per Win) + (Probability of Losing * Amount Lost per Loss)

In this case, the probability of winning is 90% or 0.9 and the amount won per win is $100. The probability of losing is 10$0 (since you don't lose any money if you don't win).

So, the expected value of the lottery is:

Expected Value = (0.9 * $100) + (0.1 *$0) = $90

This means that, on average, you can expect to win $90 every time you play this lottery. Therefore, you should be willing to pay at most$90 to play this lottery. If you pay more than this, you would be losing money in the long run.