document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=677138>Question 677138</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	A test consists of 25 multiple-choice questions. Assume that a test taker randomly guesses a choice for each and every question. Clearly state what probability model(s) you use and what value each parameter is equal to.\r<BR>\n" );
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document.write( "1 (10 points).	If each and every question has 3 choices (one correct, two incorrect), what is the probability that the test taker will get a B or better (i.e., 80 points or higher)?\r<BR>\n" );
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document.write( "2 (10 points).	If fifteen questions has three choices each (one correct, two incorrect) and ten has two choices each (one correct, one incorrect), what is the probability that the test taker will get a B or better?\r<BR>\n" );
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document.write( "I used the Binomial Probability equation (n!/(k!(n-k)!)*(p^k)*(1-p)^(n-k) for the first problem and it looks as if it works, however I don't think that this equation applies to the second question. Any suggestions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420718 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=420718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A test consists of 25 multiple-choice questions. Assume that a test taker randomly guesses a choice for each and every question. Clearly state what probability model(s) you use and what value each parameter is equal to. \r<BR>\n" );
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document.write( "1 (10 points). If each and every question has 3 choices (one correct, two incorrect), what is the probability that the test taker will get a B or better (i.e., 80 points or higher)?<BR>\n" );
document.write( "Binomial Problem with n = 25 ; p(correct) = 1/3 ; p(incorrect) = 2/3<BR>\n" );
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document.write( "Note: 80% of 25 = 20<BR>\n" );
document.write( "P(x >- 20) = 1 - binomcdf(25,1/3,19) = 0.000002269\r<BR>\n" );
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document.write( "2 (10 points). If fifteen questions has three choices each (one correct, two incorrect) and ten has two choices each (one correct, one incorrect), what is the probability that the test taker will get a B or better?<BR>\n" );
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document.write( "Need 20 correct out of 25 ; same as miss 5 or less out of 25<BR>\n" );
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document.write( "P(x <= 5 wrong) means <BR>\n" );
document.write( "5 wrong from 15 and 0 wrong from 10::::15C5(2/3)^5*(1/3)^10*10C0(1/2)^10<BR>\n" );
document.write( "or 4 wrong from 15 and 1 wrong from 10::::15C4(2/3)^4(1/3)*10C1(1/2)10<BR>\n" );
document.write( "or 3 wrong from 15 and 2 wrong from 10etc<BR>\n" );
document.write( "or 2 wrong from 15 and 3 wrong from 10<BR>\n" );
document.write( "or 1 wrong from 15 and 4 wrong from 10<BR>\n" );
document.write( "or 0 wrong from 15 and 5 wrong from 10<BR>\n" );
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document.write( "Add those products to get P(less than or equal to 5 wrong)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  <BR>\n" );
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