document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475934>Question 475934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An exam has ten true-false questions. A student who has<BR>\n" );
document.write( "not studied answers all ten questions by just guessing. Find<BR>\n" );
document.write( "the probability that the student correctly answers the given<BR>\n" );
document.write( "number of questions.<BR>\n" );
document.write( "(a) All ten questions<BR>\n" );
document.write( "(b) Exactly seven questions\r<BR>\n" );
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document.write( "thankyou! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326381 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=326381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a binomial distribution problem. Recall that the pdf of a binomial distribution for n number of trials with probability p is\r<BR>\n" );
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document.write( "P(X = x) = (n C x)*(p)^x*(1-p)^(n-x)\r<BR>\n" );
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document.write( "For more help with binomial distributions, see <a  rel=nofollow HREF=\"http://stattrek.com/tables/binomial.aspx\">this calculator</a>.\r<BR>\n" );
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document.write( "In this case, n = 10 (ie there are 10 trials since there are 10 questions) and p=1/2=0.5\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "In part a), x = 10 (since we want to get all 10 correct)\r<BR>\n" );
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document.write( "P(X = 10) = (10 C 10)*(0.5)^(10)*(1-0.5)^(10-10) \r<BR>\n" );
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document.write( "P(X = 10) = (10 C 10)*(0.5)^(10)*(0.5)^(10-10) \r<BR>\n" );
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document.write( "Note: 10 C 10 = (10!)/(10!(10-10)!) = 1\r<BR>\n" );
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document.write( "P(X = 10) = (1)*(0.5)^(10)*(0.5)^0 \r<BR>\n" );
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document.write( "P(X = 10) = (1)*(0.0009765625)*(1) \r<BR>\n" );
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document.write( "P(X = 10) = 0.0009765625\r<BR>\n" );
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document.write( "So the probability of getting all 10 correct is 0.0009765625 (which is roughly 0.098 % .... a very very small chance)\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "In part b), x = 7 (since we want exactly 7)\r<BR>\n" );
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document.write( "P(X = 7) = (10 C 7)*(0.5)^(7)*(1-0.5)^(10-7) \r<BR>\n" );
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document.write( "P(X = 7) = (10 C 7)*(0.5)^(7)*(0.5)^(10-7) \r<BR>\n" );
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document.write( "Note: 10 C 7 = (10!)/(7!(10-7)!) = 120\r<BR>\n" );
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document.write( "P(X = 7) = (120)*(0.5)^(7)*(0.5)^3 \r<BR>\n" );
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document.write( "P(X = 7) = (120)*(0.0078125)*(0.125) \r<BR>\n" );
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document.write( "P(X = 7) = 0.1171875\r<BR>\n" );
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document.write( "So the probability of getting exactly 7 correct is 0.1171875 (which is roughly 11.72%)\r<BR>\n" );
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document.write( "For more help with binomial distributions, see <a  rel=nofollow HREF=\"http://stattrek.com/tables/binomial.aspx\">this calculator</a>. </SPAN>\n" );
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