SOLUTION: Infinte Jackpot is a lottery game. 50 balls numbered 1 through 50 are placed in a machine and 4 of them are drawn at random. If the 4 numbers drawn match the numbers that a player
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-> SOLUTION: Infinte Jackpot is a lottery game. 50 balls numbered 1 through 50 are placed in a machine and 4 of them are drawn at random. If the 4 numbers drawn match the numbers that a player
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Question 1155685: Infinte Jackpot is a lottery game. 50 balls numbered 1 through 50 are placed in a machine and 4 of them are drawn at random. If the 4 numbers drawn match the numbers that a player had chosen, the player wins $50,000. In this lottery, the order the numbers are drawn in doesn’t matter. It costs 5 dollars to play. Compute the probability that you win the prize if you purchase a single lottery ticket. Also, calculate the expected value of this game. And determine whether it is a fair game. Answer by ikleyn(52776) (Show Source):
The number of all quadruples of 4 numbered balls, randomly chosen from 50 numbered balls is
= = 230300.
Of them, ONLY ONE group of balls is winning.
So the probability to win is .
In all other 230300-230299 cases the gamer loses.
Therefore. math expectation of the game is = -4.78 dollars.
So, if you play this game MANY TIMES, you should expect to lose 4.78 dollars in each game, as average.
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The analysis is completed.
For your safety, DO NOT PLAY THIS GAME (!)
-------------- Comment from student: can you show the steps on how to calculate the expected value, pls?!
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My response.
Look into this Wikipedia article
https://en.wikipedia.org/wiki/Expected_value
and read couple of lines in the section "Definition. Finite case".