SOLUTION: Find the expected payback for a game in which you bet ​$4 on any number from 0 to 399. If your number comes​ up, you get ​$500.

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Question 1149812: Find the expected payback for a game in which you bet ​$4 on any number from 0 to 399. If your number comes​ up, you get ​$500.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


399/400 chance of losing the $4 bet; 1/400 chance of making the $4 bet and winning $500, a gain of $496. The expected payback is



The expected payback is -$2.75.

Although it doesn't use the formal mathematical definition of expected value, you can determine the expected value with a simpler calculation.

You win one game in 400;
it costs $4 for each play, for a total of $1600 for the 400 games;
you win $500 once.

Your payback for the 400 games is -$1600 + $500 = -$1100; the expected payback (per game) is -$1100/400 = -$2.75.