document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463713>Question 463713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student takes a 20 question, multiple choice exam with 5 choices for each question. If the student is guessing, find the following probabilities:<BR>\n" );
document.write( "A. Getting less than 5 questions right?<BR>\n" );
document.write( "B. Passing the exam with at least an 80% score?<BR>\n" );
document.write( "C. Getting every question but 2 wrong?<BR>\n" );
document.write( "Please help?!? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317700 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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/cgi-bin/show-face.mpl?user=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let X = number of correct answers in a 20-multiple choice questions.<BR>\n" );
document.write( "X~Binomial(n=20, p=0.2)<BR>\n" );
document.write( "There are 5 choices so the probability of success is 1/5 or 0.2 and the probability of failure is 1-0.2 = 0.8.<BR>\n" );
document.write( "Therefore, the pmf of X is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+%28matrix%282%2C1%2C+20%2C+x%29%29%2A%280.2%29%5Ex%2A%280.8%29%5E%2820-x%29 ALIGN=MIDDLE  ALT=\"p%28x%29+=+%28matrix%282%2C1%2C+20%2C+x%29%29%2A%280.2%29%5Ex%2A%280.8%29%5E%2820-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the pmf we can now solve problems A,B, and C.\r<BR>\n" );
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document.write( "A.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X%3C5%29+=+sum%28+%28matrix%282%2C1%2C+20%2C+x%29%29%2A%280.2%29%5Ex%2A%280.8%29%5E%2820-x%29%2C+x+=+0%2C+x+=+4+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.6296<BR>\n" );
document.write( "B. 80% of 20 is 16 so we compute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X%3E=16%29+=+sum%28+%28matrix%282%2C1%2C+20%2C+x%29%29%2A%280.2%29%5Ex%2A%280.8%29%5E%2820-x%29%2C+x+=+16%2C+x+=+20+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, the result is a very small number close to zero.\r<BR>\n" );
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document.write( "C. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2818%29+=+%28matrix%282%2C1%2C+20%2C+18%29%29%2A%280.2%29%5E18%2A%280.8%29%5E2 ALIGN=MIDDLE  ALT=\"p%2818%29+=+%28matrix%282%2C1%2C+20%2C+18%29%29%2A%280.2%29%5E18%2A%280.8%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the result is also a very small number close to zero.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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