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

Question

10% ChanceWin 0 9090% ChanceWin 100  I am willing to pay at most                                              $ to play the lottery.

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Solution

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.Theprobabilityoflosingis10100. The probability of losing is 10% or 0.1 and the amount lost per loss is 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)+(0.1100) + (0.1 * 0) = $90

This means that, on average, you can expect to win 90everytimeyouplaythislottery.Therefore,youshouldbewillingtopayatmost90 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.

This problem has been solved

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