Algebra.Com's Answer #817272 by ikleyn(52866)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A piece of equipment contains six identical items and it is known that three of them are defective.
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document.write( "The items are tested one after the other until the three defective items are found.
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document.write( "(a) What is the probability that the testing process is stopped on the (i) third test (ii) fourth test.
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document.write( "(b) If the process is stopped on the fourth test, what is the probability that the first item is not defective?
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document.write( "(a,i) If the testing process is stopped on the third item, it means that the first item was defective, second item\r\n" );
document.write( " was defective and third item was defective. The probability of this event is\r\n" );
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document.write( " P =  =  . ANSWER\r\n" );
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document.write( "(a,ii) If the testing process is stopped on the fourth item, it may happen in these three cases, shown by sequences\r\n" );
document.write( " of letters\r\n" );
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document.write( " nDDD, DnDD, DDnD\r\n" );
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document.write( " where \"n\" symbolizes non-defective item, \"D\" sympolises defective item. So,\r\n" );
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document.write( " P(process is stopped on the fourth item) = P(nDDD) + P(DnDD) + P(DDnD).\r\n" );
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document.write( " Next, P(nDDD) =  =  =  = ; \r\n" );
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document.write( " P(DnDD) = = ;\r\n" );
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document.write( " P(DDnD) =  =  = \r\n" );
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document.write( " Thus final probability P(process is stopped on the fourth item) = + + =  . ANSWER\r\n" );
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document.write( "(b) If the testing process is stopped on the fourth item, it means that one of the three cases nDDD, DnDD, or DDnD happens,\r\n" );
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document.write( " which has the probability of , as it is shown in part (a,ii) above.\r\n" );
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document.write( " If at the same time, the first item is not defective, it means that the event nDDD did not happens, but one of DnDD or DDnD happens,\r\n" );
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document.write( " which has the probability + =  .\r\n" );
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document.write( " THEREFORE, the conditional probability under given question is P =  =  . ANSWER\r\n" );
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document.write( "Solved.\r
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document.write( "Really good probability problem.\r
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