document.write( "Question 1129379: Please help. A multiple choice test has 20 questions. Each question has five possible answers, of which one is correct. If a student guesses on every question, find the probability of getting 12 correct. \n" ); document.write( "

Algebra.Com's Answer #745938 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "    Imagine that for each of the 20 multiple choice questions the answers are labeled by 5 letters A, B, C, D and E  \r\n" );
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document.write( "    (5 possible answers to each question).\r\n" );
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document.write( "     By answering to each question, you mark your answer by one of the 5 letters.\r\n" );
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document.write( "     So, by answering to 20 questions, you write the word of the length 20, using one of 5 letters in each of the 20 positions.\r\n" );
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document.write( "     It is your model. The entire space of events consists of all  such words of the length 20, written in 5-letter alphabet.\r\n" );
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document.write( "         Now I am ready to answer the problem's questions.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If a student guesses on every question, find the probability of getting 12 correct.\r
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document.write( "So the student put correct marks (selects correct letter answer) in 12 cases and selects incorrect letter answers in 20-12 = 8 cases.\r\n" );
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document.write( "Giving incorrect answers, the student has 4 opportunity for each multiple choice questions, or, in all,  possibilities.\r\n" );
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document.write( "Thus the probability under the question is this value  \r\n" );
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document.write( "           =  = 8.65E-5 =  = 0.0000865  (approximately).\r\n" );
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