document.write( "Question 1208793: The probability of Janet winning a hockey match is 3/2 times the probability of Chrissy winning a cricket match. The probability of Jack winning a race is twice the probability of Chrissy winning the cricket match. What is the maximum probability of Janet winning the hockey match?\r
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Algebra.Com's Answer #847246 by ikleyn(52915)\"\" \"About 
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\n" ); document.write( "The probability of Janet winning a hockey match is 3/2 times the probability of Chrissy winning a cricket match.
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document.write( "Let x be the probability of Janet   winning a hockey match;\r\n" );
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document.write( "    y be the probability of Chrissy winning a cricket match;\r\n" );
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document.write( "    z be the probability of Jack    winning a race.\r\n" );
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document.write( "From the problem, we have these equalities and inequalities\r\n" );
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document.write( "    x = \"%283%2F2%29y\",               (1)\r\n" );
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document.write( "    z = 2y,                   (2)\r\n" );
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document.write( "     x <= 1, y <= 1, z<= 1.   (3)    <<<---===  general property of all probabilities . . . \r\n" );
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document.write( "Hence,  \"%283%2F2%29y\" <= 1,  which means  y <= \"2%2F3\".         (4)\r\n" );
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document.write( "Also    z = 2y <= 1,  which implies  y <= \"1%2F2\".        (5)\r\n" );
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document.write( "Comparing (4) and (5), we conclude that  y <= \"1%2F2\".\r\n" );
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document.write( "Due to (1), it implies then that  x <= \"%283%2F2%29%2A%281%2F2%29\" = \"3%2F4\".\r\n" );
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document.write( "It gives the final ANSWER :  the maximum probability of Janet winning the hockey match is  \"3%2F4\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Good entertainment problem.\r
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\n" ); document.write( "\n" ); document.write( "It teaches on how to find a core idea, how to start in a right way
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\n" ); document.write( "\n" ); document.write( "It was a pleasure to me to solve it.   Thank you for posting it  ( ! )\r
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