document.write( "Question 1138185: Joe is playing a game of chance at the hibiscus festival, costing $1 for each game. In the game two fair dice are rolled and the sum of the numbers that turned up is found. If the sum is seven, then Joe wins $5. Otherwise loses his money. Joe play the game 15 times. Find his expected profit or lose. \n" ); document.write( "

Algebra.Com's Answer #756036 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "When two fair dice are rolled, there are 36 possible outcomes, each with the probability of  .\r\n" );
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document.write( "These outcomes are the pairs of integer numbers (i,j), where i and j take independently the values from 1 to 6.\r\n" );
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document.write( "The number of such pairs with the sum i+j = 7 is  6\r\n" );
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document.write( "( the pairs are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1) ).\r\n" );
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document.write( "So, the probability to get the sum of 7 at each roll of a pair of dice is   = .\r\n" );
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document.write( "Mathematical expectation of the amount of money to win at each roll of a pair of dice is   dollars,\r\n" );
document.write( "but Joe should pay one dollar for each roll,\r\n" );
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document.write( "so his expected profit at each roll of a pair of dice is\r\n" );
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document.write( "     =  =   of a dollar.\r\n" );
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document.write( "Thus, statistically, Joe should expect the loss   of a dollar in each roll of a pair of dice.\r\n" );
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document.write( "Making 15 rolls in the game, Joe should expect to lose   dollars =  dollars = $2.50.     ANSWER\r\n" );
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