document.write( "Question 1117792: A quiz has 4 multiple choice questions and each has 5 choices. What is the probability of getting at least 2 answers right by guessing? \n" ); document.write( "

Algebra.Com's Answer #732946 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "The method to solve this problem is to consider the probability of the complement set of events.\r
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\n" ); document.write( "\n" ); document.write( "The complement set of events is (to give exactly one correct answer when answering to all four multiple choice questions) ,\r
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\n" ); document.write( "\n" ); document.write( "Again: the complement set of events is (to give the correct answer to exactly one of the four multiply choice and to give incorrect
\n" ); document.write( "answers to the three other questions) or (to give incorrect answers to all 4 multiply choice questions).\r
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document.write( "    Since each of 4 multiple choice question has 5 choices, the probability to randomly guess the answer correctly \r\n" );
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document.write( "    to each of the questions is . \r\n" );
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document.write( "    Correspondingly, the probability to give randomly incorrect answer to EACH SEPARATE of the four questions is .\r\n" );
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document.write( "    Therefore, the probability to give randomly correct answer to any one fixed question and to give incorrect answer \r\n" );
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document.write( "    to all of remaining three questions is .\r\n" );
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document.write( "    It means that with four multiply choice questions, to give the correct answer to one of the four multiply choice and to give incorrect \r\n" );
document.write( "    answer to the three other questions is four time of that, i.e.\r\n" );
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document.write( "     =     (*)\r\n" );
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document.write( "    Very good.  Now, the probability to give all 4 incorrect answers to all 4 questions is  .           (**)\r\n" );
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document.write( "    Then the final probability under the question is the complement to the sum of (*)  and (**):\r\n" );
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document.write( "    1 -  -  = 0.1808 = 18.08%.\r\n" );
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