SOLUTION: In a lottery game, a player picks six numbers from 1 to 24. If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1. What is the expected value o

Algebra ->  Probability-and-statistics -> SOLUTION: In a lottery game, a player picks six numbers from 1 to 24. If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1. What is the expected value o      Log On


   



Question 1206157: In a lottery game, a player picks six numbers from 1 to 24. If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1.
What is the expected value of this game?

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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In a lottery game, a player picks six numbers from 1 to 24.
If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1.
What is the expected value of this game?
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The number of all possible sextuples of numbers from 1 to 24, without repetitions, is

C%5B24%5D%5E6 = %2824%2A23%2A22%2A21%2A29%2A19%29%2F%281%2A2%2A3%2A4%2A5%2A6%29 = 134596.


So, the probability for the player to get the winning sextuple is  1%2F134596.


Therefore, the expected value of the game is

    30000%2F134596 - 1 = -0.777110761  dollars.


It means that a player loses, in average, 0.777110761 of a dollar 
if plays this game many times.

Solved.