document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #778326 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "The number of all quadruples of 4 numbered balls, randomly chosen from 50 numbered balls is\r\n" );
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document.write( "     =  = 230300.\r\n" );
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document.write( "Of them, ONLY ONE group of balls is winning.\r\n" );
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document.write( "So the probability to win is  .\r\n" );
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document.write( "In all other  230300-230299 cases the gamer loses.\r\n" );
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document.write( "Therefore. math expectation of the game is   = -4.78 dollars.\r\n" );
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document.write( "So, if you play this game MANY TIMES, you should expect to lose  4.78 dollars in each game, as average.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The analysis is completed.\r
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\n" ); document.write( "\n" ); document.write( "For your safety, DO NOT PLAY THIS GAME (!)\r
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\n" ); document.write( "Comment from student: can you show the steps on how to calculate the expected value, pls?!
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\n" ); document.write( "\n" ); document.write( "My response.\r
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\n" ); document.write( "\n" ); document.write( "Look into this Wikipedia article\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Expected_value\r
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\n" ); document.write( "\n" ); document.write( "and read couple of lines in the section \"Definition. Finite case\".\r
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