90% ChanceWin of 0 $10% ChanceWin of 100 $ I am willing to pay at most $ to play the lottery.
Question
90% Chance Win of $0
10% Chance Win of $100
I am willing to pay at most
$
to play the lottery.
Solution
The amount you should be willing to pay to play the lottery can be calculated using the concept of Expected Value in probability.
The Expected Value (EV) is calculated as follows:
EV = (Probability of Outcome 1 * Value of Outcome 1) + (Probability of Outcome 2 * Value of Outcome 2) + ... + (Probability of Outcome n * Value of Outcome n)
In this case, there are two possible outcomes:
- Winning $0 with a 90% chance
- Winning $100 with a 10% chance
So, the Expected Value would be:
EV = (0.90 * 100) = 10 = $10
Therefore, you should be willing to pay at most $10 to play the lottery. If you pay more than this, on average, you would be losing money.
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