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

Algebra ->  Probability-and-statistics -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
.

The number of all quadruples of 4 numbered balls, randomly chosen from 50 numbered balls is

    C%5B50%5D%5E4 = %2850%2A49%2A48%2A47%29%2F%281%2A2%2A3%2A4%29 = 230300.


Of them, ONLY ONE group of balls is winning.


So the probability to win is  1%2F230300.


In all other  230300-230299 cases the gamer loses.


Therefore. math expectation of the game is  50000%2F230300+-+5 = -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 (!)



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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".