We place ourself now in the two-digit lottery. Condition of the game is as the Following. Suppose that a man bets one dollar. If he chooses the right number he will get 70 dollars, otherwise he will lose one dollar. Question: if a man decides to play this game, how much does he expect to gain/lose?
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There are 10 possible values for each digit of the PIN (namely: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9), so there are 10 × 10 × 10 × 10 = 104 = 10000 total possible PINs.
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