document.write( "Question 698174: ) Of two men, it is said that
\n" ); document.write( "one sometimes tells the truth
\n" ); document.write( "while the other only tells the
\n" ); document.write( "truth two times out of three. If
\n" ); document.write( "one is chosen at random. ... at
\n" ); document.write( "random and asked a question,
\n" ); document.write( "the probability of a truthful
\n" ); document.write( "answer is 17/24.how often does the man tell the truth
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Algebra.Com's Answer #430587 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
probability that the man you ask is the one who tells the truth 2 times out of 3 = \"1%2F2\"
\n" ); document.write( "\"2%2F3\" = probability of getting a true answer if you ask that guy.
\n" ); document.write( "probability that the man you ask is the other man = \"1%2F2\"
\n" ); document.write( "\"x\" = fraction of the times the other man tells the truth
\n" ); document.write( "(in other words the probability that his answer would be true).
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\n" ); document.write( "If you ask one of the two men a question, your probability of getting a true answer is
\n" ); document.write( "\"%281%2F2%29%2A%282%2F3%29%2B%281%2F2%29%2Ax=17%2F24\"
\n" ); document.write( "\"1%2F3%2B%281%2F2%29%2Ax=17%2F24\"
\n" ); document.write( "\"%281%2F2%29%2Ax=17%2F24-1%2F3\"
\n" ); document.write( "\"%281%2F2%29%2Ax=17%2F24-8%2F24\"
\n" ); document.write( "\"%281%2F2%29%2Ax=9%2F24\"
\n" ); document.write( "\"2%2A%281%2F2%29%2Ax=2%2A%289%2F24%29\" --> \"x=9%2F12%29\" --> \"highlight%28x=3%2F4%29\"
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