document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33820>Question 33820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A coin is tossed continuously until either a head turns up or a total of three tails comes up.What is the expected number of tosses for this event? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20885 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=20885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The head comes up either on the 1st toss, or the 2nd toss or on the 3rd<BR>\n" );
document.write( "toss. If no head on 1,2, or 3 we have ttt so we are finished.<BR>\n" );
document.write( "Take each case; count the number of tosses involved; multiply by the probability of this particular case. Then add up the products to get the<BR>\n" );
document.write( "expected value.\r<BR>\n" );
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document.write( "Here we go:<BR>\n" );
document.write( "h    number of tosses=1   probability of this = 1/2; product = 1(1/2)= 1/2<BR>\n" );
document.write( "th   number of tosses=2    prob of this is 1/4;  product is 2(1/4)= 1/2<BR>\n" );
document.write( "tth  number of tosses=3    prob of this is 1/8;  product is 3(1/8)=3/8<BR>\n" );
document.write( "ttt  number of tosses=3    prob of this is 1/8;  product is 3(1/8)=3/8<BR>\n" );
document.write( "Expected value = 1/2 + 1/2 + 3/8 + 3/8= 14/8=7/4=1.75 tosses<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );