document.write( "Question 1142909: The probability that a student passes a class is
\n" ); document.write( "p(P) = 0.55.
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\n" ); document.write( "p(S) = 0.51.
\n" ); document.write( " The probability that a student passes a class given that he or she studied for the class is
\n" ); document.write( "p(P / S) = 0.70.\r
\n" ); document.write( "\n" ); document.write( " What is the probability that a student studied for the class, given that he or she passed the c\r
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Algebra.Com's Answer #763936 by ikleyn(52852) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by @srimankumar45 is partly incorrect and partly unreadable.\r
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\n" ); document.write( "\n" ); document.write( "            I came to bring a correct solution.\r
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\n" ); document.write( "\n" ); document.write( "            I will solve the problem in two steps.\r
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\n" ); document.write( "\n" ); document.write( "            Trace attentively my steps to see the difference with the other tutor' solution.\r
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document.write( "(a)  The first step is to find  p(P & S).   ( which is the same as  p(P intersection S) )\r\n" );
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document.write( "         p(P | S) = p(P & S)/p(S)     (by the definition of the conditional probability)\r\n" );
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document.write( "     It gives\r\n" );
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document.write( "         0.70 = p(P & S) /0.51,  \r\n" );
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document.write( "         p(P & S) = 0.70*0.51.\r\n" );
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document.write( "(b)  The second step is to get the answer to the problem' question.\r\n" );
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document.write( "         p(S | P) = p(S & P)/p(P)     (by the definition of the conditional probability)\r\n" );
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document.write( "     Notice that p(S & P) = p(P & S) = 0.70*0.51,  as we found it in (a).\r\n" );
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document.write( "     Therefore,  \r\n" );
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document.write( "         p(S | P) =  = 0.649   (approximately)   ANSWER\r\n" );
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