document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082101>Question 1082101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A coin is biased such that the head is twice as likely to occur as tail. If this coin is tossed 4 times, find<BR>\n" );
document.write( "i- the sample space<BR>\n" );
document.write( "ii- the probability of having at least 2 heads<BR>\n" );
document.write( "iii- the probability of having exactly 3 heads<BR>\n" );
document.write( "iv- the probability of having at most 4 heads. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696177 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=696177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> HHHH<BR>\n" );
document.write( "HHHT<BR>\n" );
document.write( "HHTH<BR>\n" );
document.write( "HTHH<BR>\n" );
document.write( "THHH<BR>\n" );
document.write( "HHTT<BR>\n" );
document.write( "HTHT<BR>\n" );
document.write( "HTTH<BR>\n" );
document.write( "THHT<BR>\n" );
document.write( "THTH<BR>\n" );
document.write( "TTHH<BR>\n" );
document.write( "TTTH<BR>\n" );
document.write( "TTHT<BR>\n" );
document.write( "THTT<BR>\n" );
document.write( "HTTT<BR>\n" );
document.write( "TTTT<BR>\n" );
document.write( "Exactly two heads in 4 tosses: 6 ways of having them 4C2<BR>\n" );
document.write( "The denominator of the product of the probabilities is always 81.  The numerator numbers change in order but not in product, and they are 2*2*1*1=4.  Multiply by 6 and get 24/81=8/27<BR>\n" );
document.write( "exactly 3 heads is 4 * 2*2*2*1/87=32/81<BR>\n" );
document.write( "exactly 4 heads is 2*2*2*2/81=16/81<BR>\n" );
document.write( "(and 1 head and 0 heads for completeness:<BR>\n" );
document.write( "1:2*4/81=8/81<BR>\n" );
document.write( "0:1/81<BR>\n" );
document.write( "Sum is 81/81 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );