document.write( "Question 969131: A multiple choice test has 10 questions. Each question has four answer choices. \r
\n" ); document.write( "\n" ); document.write( "a. What is the probability a student randomly guesses the answers and gets exactly six questions correct?\r
\n" ); document.write( "\n" ); document.write( "b. Is getting exactly 10 questions correct the same probability as getting exactly zero correct? Explain.\r
\n" ); document.write( "\n" ); document.write( " c. Describe the steps needed to calculate the probability of getting at least six questions correct if the student randomly guesses. You do not need to calculate this probability!\r
\n" ); document.write( "\n" ); document.write( "It would be greatly appreciated if you could show work as to how to solve these, thanks! \n" ); document.write( "
Algebra.Com's Answer #592188 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Binomial probability:\r\n" );
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document.write( "The probability of getting exactly x successes out of n trials, when\r\n" );
document.write( "the probability of getting 1 success in 1 trial is p is given by the\r\n" );
document.write( "formula \"%28matrix%282%2C1%2Cn%2Cx%29%29%2A%28p%29%5Ex%281-p%29%5E%28n-x%29\".\r\n" );
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document.write( "Notice that \"%28matrix%282%2C1%2Cn%2Cx%29%29\" is also written as nCx or C(n,x) or\r\n" );
document.write( "the number of combinations of n things taken x at a time.\r\n" );
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document.write( "This can also be found with a TI-83 or 84 graphing calculator, press\r\n" );
document.write( "2ND VARS to find binompdf(n,p,x). Put in numbers for n,p, and x.\r\n" );
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\n" ); document.write( "A multiple choice test has 10 questions. Each question has four answer choices. \r
\n" ); document.write( "\n" ); document.write( "a. What is the probability a student randomly guesses the answers and gets exactly six questions correct?
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document.write( "That's the binomial probability of getting exactly 6 successes in 10 trials with\r\n" );
document.write( "the probability of 1 success in 1 trial of 1/4.\r\n" );
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document.write( "\"%28matrix%282%2C1%2C10%2C6%29%29%2A%281%2F4%29%5E6%283%2F4%29%5E%2810-6%29\"\"%22%22=%22%22\"\".0162220001\"\r\n" );
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\n" ); document.write( "b. Is getting exactly 10 questions correct the same probability as getting
\n" ); document.write( "exactly zero correct? Explain.
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document.write( "No.  Although both are very unlikely, it is 3 times as likely to guess an answer\r\n" );
document.write( "incorrectly than to guess it correctly.  So it is more likely to guess them all\r\n" );
document.write( "incorrectly than all correctly.  (However, in a true-false test, they would be\r\n" );
document.write( "the same.)   \r\n" );
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\n" ); document.write( "c. Describe the steps needed to calculate the probability of getting at least
\n" ); document.write( "six questions correct if the student randomly guesses. You do not need to
\n" ); document.write( "calculate this probability!
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document.write( "You would do these steps:\r\n" );
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document.write( "1. Calculate the probability of getting exactly 6 correct.\r\n" );
document.write( "\"%28matrix%282%2C1%2C10%2C6%29%29%2A%281%2F4%29%5E6%283%2F4%29%5E%2810-6%29\"\"%22%22=%22%22\"\".0162220001\"\r\n" );
document.write( "2. Calculate the probability of getting exactly 7 correct.\r\n" );
document.write( "\"%28matrix%282%2C1%2C10%2C7%29%29%2A%281%2F4%29%5E7%283%2F4%29%5E%2810-7%29\"\"%22%22=%22%22\"\".0030899048\"\r\n" );
document.write( "3. Calculate the probability of getting exactly 8 correct.\r\n" );
document.write( "\"%28matrix%282%2C1%2C10%2C8%29%29%2A%281%2F4%29%5E8%283%2F4%29%5E%2810-8%29\"\"%22%22=%22%22\"\".0003862380981\"\r\n" );
document.write( "4. Calculate the probability of getting exactly 9 correct.\r\n" );
document.write( "\"%28matrix%282%2C1%2C10%2C9%29%29%2A%281%2F4%29%5E9%283%2F4%29%5E%2810-9%29\"\"%22%22=%22%22\"\".00002861022949\"\r\n" );
document.write( "5. Calculate the probability of getting all 10 correct.\r\n" );
document.write( "\"%28matrix%282%2C1%2C10%2C10%29%29%2A%281%2F4%29%5E10%283%2F4%29%5E%2810-10%29\"\"%22%22=%22%22\"\".0000009536743164\"\r\n" );
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document.write( "Then you would add them all up and you'd get: .0197277069\r\n" );
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document.write( "Edwin
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