document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105419>Question 1105419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An exam was applied with 10 questions of multiple choice, with four options each, being only one correct. John took the exam without knowing anything, answering the questions at random.<BR>\n" );
document.write( "a) What is the probability of John to solve four questions?<BR>\n" );
document.write( "b) What is the probability that John scores more than 50% of the exam?<BR>\n" );
document.write( "c) John's mother promised $ 100 if he takes out 9 or 10, or $ 50 if he takes 7 or 8. If he draws below 7, it goes without premium. Calculate the expected gain of John.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720230 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720230\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Getting 4 correct is 10C4(1/4)^4(3/4)^6=0.1460.<BR>\n" );
document.write( "Scores more than 50% means getting 6 or more right.<BR>\n" );
document.write( "Getting 6 right is 210(.25^6)(.75^4)=0.0162; 7 right is 120*.25^7*.75^3=0.003; 8 right 0.0004, 9 right is <0.0001, so the probability is 0.0196\r<BR>\n" );
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document.write( "Expected value is X*p(X), so it is $100* probability of 9 or 10+ $50 for probability of 7 or 8.<BR>\n" );
document.write( "9 or 10 right is 0.00003 and 10 right is 0.000001, for 0.0000031, the probability for $100=0.000095<BR>\n" );
document.write( "for 7 and 8, the probability is 0.0034.  Multiply by $50  to get $0.17. That is the answer given the results for 9 and 10.\r<BR>\n" );
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