document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930996>Question 930996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the probability of missing no more than 1 question by guessing on a 8 total true or false question test? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #565394 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=565394\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a binomial distribution question.\r<BR>\n" );
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document.write( "n = 8<BR>\n" );
document.write( "p = 1/2 = 0.5\r<BR>\n" );
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document.write( "Let's define the function B(k) to be the probability where the student misses k problems where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=k%3C=8 ALIGN=MIDDLE  ALT=\"0%3C=k%3C=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it's defined in terms of the <a  rel=nofollow HREF=\"http://stattrek.com/probability-distributions/binomial.aspx\">binomial distribution formula</a>\r<BR>\n" );
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document.write( "B(k) = (n C k)*p^k*(1-p)^(n-k)\r<BR>\n" );
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document.write( "Let's plug in the constants n = 8 and p = 0.5 to get\r<BR>\n" );
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document.write( "B(k) = (8 C k)*0.5^k*(1-0.5)^(8-k)<BR>\n" );
document.write( "B(k) = (8 C k)*0.5^k*0.5^(8-k)\r<BR>\n" );
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document.write( "Since it asks \"what is the probability of missing no more than 1 question\" we want to find P(X <= 1) which means we need to evaluate B(0) and B(1). Then we add up those two values\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3C=+1%29+=+B%280%29+%2B+B%281%29 ALIGN=MIDDLE  ALT=\"P%28X+%3C=+1%29+=+B%280%29+%2B+B%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "P(Missing 0) = B(0) = (8 C 0)*(0.5^0)*(0.5)^(8-0) = 0.00390625\r<BR>\n" );
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document.write( "P(Missing 1) = B(1) = (8 C 1)*(0.5^1)*(0.5)^(8-1) = 0.03125\r<BR>\n" );
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document.write( "Now add up the two individual probabilities (PDF's) to get the cumulative probability (CDF)\r<BR>\n" );
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document.write( "B(0) + B(1) = 0.00390625+0.03125 = 0.03515625\r<BR>\n" );
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document.write( "P(X <= 1) = 0.03515625\r<BR>\n" );
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document.write( "So the probability of missing no more than 1 question is <font color=\"red\">0.03515625</font>\r<BR>\n" );
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document.write( "If you need more one-on-one help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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