document.write( "Question 1051952: A quiz consists of 6 multiple-choice questions. Each question has 4 possible answers. A
\n" ); document.write( "student is unprepared, and he has no choice but guessing answers completely at random.
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Algebra.Com's Answer #667410 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "The probability that he will guess an answer right is 1/4.\r\n" );
document.write( "The probability that he will guess an answer wrong is 3/4.\r\n" );
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document.write( "This is a cumulative binomial probability where the number of trials \r\n" );
document.write( "is n=6, with the probability of a success in 1 trial is 1/4.\r\n" );
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document.write( "With a TI-83 or 84,  it's 1-binomcdf(6,1/4,2). Ans: 0.1694335937\r\n" );
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document.write( "Or without a calculator that has binomial probability feature:\r\n" );
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document.write( "Case 1: Guessing exactly 3 correct:\r\n" );
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document.write( "Choosing exactly 3 to get correct = Choosing exactly\r\n" );
document.write( "3 to get wrong = 6C3 = (6*5*4)/(3*2*1) = 20 ways.\r\n" );
document.write( "Guess the wrong answer for the first wrong one 3 ways.\r\n" );
document.write( "Guess the wrong answer for the second wrong one 3 ways.\r\n" );
document.write( "Guess the wrong answer for the third wrong one 3 ways.\r\n" );
document.write( "That's 20×3×3×3 = 540 ways\r\n" );
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document.write( "Case 2: Guessing exactly 4 correct:\r\n" );
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document.write( "Choosing exactly 4 to get correct = Choosing exactly\r\n" );
document.write( "2 to get wrong = 6C2 = (6*5)/(2*1) = 15 ways.\r\n" );
document.write( "Guess the wrong answer for the first wrong one 3 ways.\r\n" );
document.write( "Guess the wrong answer for the second wrong one 3 ways.\r\n" );
document.write( "That's 15×3×3 = 135 ways\r\n" );
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document.write( "Case 3: Guessing exactly 5 correct:\r\n" );
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document.write( "Choosing exactly 5 to get correct = Choosing exactly\r\n" );
document.write( "1 wrong = 6C1 = 6 ways.\r\n" );
document.write( "Guess the wrong answer for the wrong one 3 ways.\r\n" );
document.write( "That's 6×3 = 18 ways\r\n" );
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document.write( "Case 4: Guessing all 6 correct\r\n" );
document.write( "There is only 1 way to guess them all correct\r\n" );
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document.write( "Total number of ways to pass: 540+135+18+1 = 694 ways to pass\r\n" );
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document.write( "Total number of ways to answer:\r\n" );
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document.write( "(4 ways to answer question 1) times\r\n" );
document.write( "(4 ways to answer question 2) times\r\n" );
document.write( "(4 ways to answer question 3) times\r\n" );
document.write( "(4 ways to answer question 4) times\r\n" );
document.write( "(4 ways to answer question 5) times\r\n" );
document.write( "(4 ways to answer question 6) equals 4×4×4×4×4×4 = 4⁶ = 4096\r\n" );
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document.write( "Edwin

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