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

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(52777) (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

     =  = 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.

-----------------

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?!
--------------

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".

RELATED QUESTIONS
Infinte Jackpot is a lottery game. 50 balls numbered 1 through 50 are placed in a machine (answered by ikleyn)

In a certain lottery, a participant must choose five numbers from 1 to 30. (The numbers... (answered by stanbon)

In a lottery game, a machine has 51 balls marked with numbers from 1-51 and six of them... (answered by Boreal)

In a state lottery 25 balls numbered from 1 to 25 and placed in machine. 6 numbers... (answered by Boreal)

A box contains 50 balls numbered from 1 to 50. If 10 balls are drawn with replacement,... (answered by stanbon,Alyrian)

In a bingo game, balls numbered 1 to 75 are placed in a bin. Balls are randomly drawn and (answered by Fombitz)

Winning tickets in a lottery are chosen by selecting 6 balls numbered 1 through 50,... (answered by ikleyn)

For a lottery drawing, balls numbered with the digits 1-9 are placed in three bins and... (answered by Alan3354,jrfrunner)

In a bingo game, balls numbered 1 to 25 are placed in a bin. Balls are randomly drawn... (answered by Alan3354)