document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124560>Question 1124560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tom has three coins. Two are fair and one is an unfair coin weighted so that heads is five times as likely as tails. He selects one of the coins at random and flips it. \r<BR>\n" );
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document.write( "What is the probability it comes up heads?  <BR>\n" );
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document.write( "If it does come up heads, what is the probability it was a fair coin?  <BR>\n" );
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document.write( "Enter your answers as whole numbers or fractions in lowest terms. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740878 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=740878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> probability of three coins coming up heads are 0.5, 0.5, and (5/6) or 0.8333<BR>\n" );
document.write( "the expected value of heads is (1/2)(1/3)*2+(5/6)(1/3)=1/3+(5/18)=(11/18) ANSWER<BR>\n" );
document.write( "P(Fair|Heads)=P(Fair)*P(H|F)/P(H)<BR>\n" );
document.write( "=(2/3)*(1/2)/(11/18)<BR>\n" );
document.write( "=(1/3)(18/11)=18/33 or 6/11 ANSWER </SPAN>\n" );
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