document.write( "Question 283657: If a gambler rolls two dice and gets a sum of 7, he wins $10, and if he gets a sum of 4, he wins $20. The cost to play the game is $5. What is the expectation (to the nearest cent) of this game? \n" ); document.write( "

Algebra.Com's Answer #205871 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
If a gambler rolls two dice and gets a sum of 7, he wins $10, and if he gets a sum of 4, he wins $20. The cost to play the game is $5. What is the expectation (to the nearest cent) of this game?
\n" ); document.write( "

\r\n" );
document.write( "There are three possible outcomes of playing the game:\r\n" );
document.write( "\r\n" );
document.write( "A. He can pay $5 to play, roll a sum of 7, win $10, and net $5.\r\n" );
document.write( "\r\n" );
document.write( "B. He can pay $5 to play, roll a sum of 4, win $20, and net $15.\r\n" );
document.write( "\r\n" );
document.write( "C. He can pay $5 to play, roll a sum of neither 4 nor 7, and net -$5 (a loss).\r\n" );
document.write( "\r\n" );
document.write( "Now we need to calculate the probabilities of doing those.\r\n" );
document.write( "\r\n" );
document.write( "Here is the sample space of rolling a pair of dice:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(1,1)   (1,2)   (1,3)   (1,4)   (1,5)   (1,6) \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2,1)   (2,2)   (2,3)   (2,4)   (2,5)   (2,6)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(3,1)   (3,2)   (3,3)   (3,4)   (3,5)   (3,6)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(4,1)   (4,2)   (4,3)   (4,4)   (4,5)   (4,6)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(5,1)   (5,2)   (5,3)   (5,4)   (5,5)   (5,6)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(6,1)   (6,2)   (6,3)   (6,4)   (6,5)   (6,6)\r\n" );
document.write( "\r\n" );
document.write( "There are 36 posasible rolls.  The 6 red ones have sum 7, the 3 blue ones\r\n" );
document.write( "have sum 4, the 27 black ones have some other sum.  So \r\n" );
document.write( "\r\n" );
document.write( "The probability of rolling a 7 is  or . P(A) = \r\n" );
document.write( "\r\n" );
document.write( "The probability of rolling a 4 is  or . P(B) = \r\n" );
document.write( "\r\n" );
document.write( "The probability of rolling neither of those sum is  or \r\n" );
document.write( "   P(C) = \r\n" );
document.write( "\r\n" );
document.write( "To find the expectation, multiply each win by the probability of winning it,\r\n" );
document.write( "then add them.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That means if one plays the game many times he will have\r\n" );
document.write( "averaged losing  cents per game.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );