Probability of winning the Buck.
A friend of your's proposes a game: if you correctly guess the amount of money in his wallet, the cash is yours. Only Single guess is allowed. You know him well, so you are sure that there'a a 50% chance of his wallet being empty. A 25% chance of $1, 24% chance of $100, And a 1% chance of $1000.
What is the guessing amount in order to maximize the Expected winning?
The answer is 100.
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1 solution
Only three guesses can win a positive amount of money: $ 1 , $ 1 0 0 , and $ 1 0 0 0 .
The expected return for a wager of $ 1 is ( 0 . 7 5 ) ∗ 0 + ( 0 . 2 5 ) ∗ $ 1 = $ 0 . 2 5 .
The expected return for a wager of $ 1 0 0 is ( 0 . 7 6 ) ∗ 0 + ( 0 . 2 4 ) ∗ $ 1 0 0 = $ 2 4 . 0 0 .
The expected return for a wager of $ 1 0 0 0 is ( 0 . 9 9 ) ∗ 0 + ( 0 . 0 1 ) ∗ $ 1 0 0 0 = $ 1 0 . 0 0 .
Thus the highest expected return is for the $ 1 0 0 bet.