document.write( "Question 1200014: A simple gambling game involves the throw of a die. Players are charged 40 cents if the die shows 1,2 or 3 they are charged nothing for 4 and they receive 30 cents or 60 cents respectively for 5 or 6. Let the random variable X be the payout to the player.
\n" ); document.write( "Calculate the expected value and how much profit would the casino expect to make on 100 games?\r
\n" ); document.write( "\n" ); document.write( "If the backer weighted the die so that it is 50% more likely to turn up each of the results 1,2,3 as to turn up 4,5 or 6.
\n" ); document.write( "What is the probability now of each outcome?
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Algebra.Com's Answer #834028 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A simple gambling game involves the throw of a die.
\n" ); document.write( "Players are charged 40 cents if the die shows 1,2 or 3 they are charged nothing
\n" ); document.write( "for 4 and they receive 30 cents or 60 cents respectively for 5 or 6.
\n" ); document.write( "Let the random variable X be the payout to the player.
\n" ); document.write( "Calculate the expected value and how much profit would the casino expect to make on 100 games?
\n" ); document.write( "If the backer weighted the die so that it is 50% more likely to turn up
\n" ); document.write( "each of the results 1,2,3 as to turn up 4,5 or 6.
\n" ); document.write( "What is the probability now of each outcome?
\n" ); document.write( "Find expected value now.
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\n" ); document.write( "\n" ); document.write( "            I agree with the solution of the first problem given by @math_tutor2020.\r
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\n" ); document.write( "\n" ); document.write( "            But regarding the second problem in the post, I read and interpret it differently; \r
\n" ); document.write( "\n" ); document.write( "            therefore, my solution, my numbers and my answer are different.\r
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document.write( "In the second problem, we have six events 1, 2, 3, 4, 5 and 6, and we are given that\r\n" );
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document.write( "    P(1) = P(2) = P(3);  P(4) = P(5) = P(6) \r\n" );
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document.write( "and \r\n" );
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document.write( "    P(1) = 1.5*P(4);  P(2) = 1.5*P(5);  P(3) = 1.5*P(6).\r\n" );
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document.write( "Let x be any of the three equal values  P(4) = P(5) = P(6).\r\n" );
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document.write( "Then any of the three other equal values  P(1) = P(2) = P(3)  is  1.5x  (it is where and how the multiplier 1.5 works in my solution).\r\n" );
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document.write( "The sum of probabilities  P(1) + . . . + P(6) is 1.  It gives this equation\r\n" );
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document.write( "    3*(1.5x) + 3x = 1,  or  4.5x + 3x = 1,  or  7.5x = 1,\r\n" );
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document.write( "which implies \r\n" );
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document.write( "    x =  = ;  1.5x =  = .\r\n" );
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document.write( "Thus  P(1) = P(2) = P(3) = ;  P(4) = P(5) = P(6) = .\r\n" );
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document.write( "Now math expectation of the player/(the gamer) is\r\n" );
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document.write( "       +  +  +  +  +  = \r\n" );
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document.write( "   =  =  cents = -12 cents.\r\n" );
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document.write( "Which means that the gamer loses 12 cents per game, in average. \r\n" );
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document.write( "ANSWER.  Math expectation is -12 cents: the gamer loses 12 cents per game, in average. \r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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