document.write( "Question 1160048: To make decisions on the purchase of securities, a market analysis system was developed. From past data it is known that 5% of the market are “bad” securities - unsuitable objects for investment. The proposed system identifies 98% of “bad” securities as potentially “bad”, but also defines 15% of eligible investments as potentially “bad”. Given that a security has been identified as potentially “bad”, what is the likelihood that the security is actually “bad”? Comment on the suitability of the system for making investment decisions. \n" ); document.write( "

Algebra.Com's Answer #783446 by ikleyn(53937) $\"\"$ $\"About$

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document.write( "Let N be the total number of all securities.\r\n" );
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document.write( "Then 0.05N of them are \"bad\" securities.    ( (!) actually \"bad\", using the terminology from the condition).\r\n" );
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document.write( "The proposed system identifies 98% of these 0.05N \"bad\" securities as potentially bad;\r\n" );
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document.write( "    so, there are 0.98*0.05N potentially bad securities, from this pool.\r\n" );
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document.write( "The system also defines 15% of the rest, eligible securities as potentially bad. \r\n" );
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document.write( "     So, there are addition 0.15*(1-0.05)N = 0.15*0.95N potentially bad securities, from the other pool.\r\n" );
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document.write( "In all, the number of potentially bad securities is the sum\r\n" );
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document.write( "     0.098*0.05N + 0.15*0.95N.\r\n" );
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document.write( "Now, the probability under the question is\r\n" );
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document.write( "    P =  =  =  = 0.339213.    ANSWER\r\n" );
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document.write( "It means that the \"proposed system\" recognizes actually bad securities among potentially bad securities with the probability about 0.34 only.\r\n" );
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document.write( "It is, actually, a  very low level recognition system.   ( It is enough to say, that it is WORST than tossing coin (!) )\r\n" );
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document.write( "At so low recognition level, it is better to vote AGAINST the system's predictions.\r\n" );
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document.write( "A good (or an ideal) system should recognize with the probability 0.9 - 0.95 - 0.98.\r\n" );
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