document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33111>Question 33111</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use a tree diagram showing all possible results when 4 fair coins are tossed. List the ways of getting more than 2 tails. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19528 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=19528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we cannot draw a tree diagram here so i shall have to try to describe it to you:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Start at the left of your page, some way down the page.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Draw 2 diagonal lines showing the 2 outsomes of the 1st coin toss. Label those as H (for Heads) and T (for tails). Against each of those, draw 2 more diagonal lines and lable them H and T twice. Remember to draw the original diagonal lines steep enough because you are going to do this at 4 different positions across the page, each denoting another toss of the coin.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "However, you are going to get a lot of repetition down the page because the tree diagram is a representation of ALL the outcomes. Getting a TAIL on the second throw has 2 \"origins\"...the first toss might have been a HEAD and then the second a TAIL OR first toss was a TAIL and second was also a TAIL.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, for something with 2 outcomes like a coin toss, we would have 2 outcomes then second event would have 4 (2 sets of 2) and then the third event would have 8 (4 sets of 2) and then the fourth event would have 16 (8 sets of 2).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As i said, i cannot draw it here, but this is the beginning of it, as much as i can do for you:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "_____H<BR>\n" );
document.write( "__H <<BR>\n" );
document.write( "<<BR>\n" );
document.write( "__T <<BR>\n" );
document.write( "_____T\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, i know this is a very bad representation...ignore the underscores as they just are there to help me position the < and the H and T.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Along each and every branch, write 0.5 as the probability. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then read of the tree going left to right, along a set of branches --> one route. Eg following along the top-most branch, we get P(head AND head AND head AND head) = 0.5 * 0.5 * 0.5 * 0.5 <BR>\n" );
document.write( "P(HHHH) = 1/16\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You will find that the probability of every route on this tree is 1/16, since all the probabilities are the same, namely 1/2 for a coin.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You will also see that there are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1 outcome of HHHH<BR>\n" );
document.write( "4 outcomes of HHHT --> HHHT, HHTH, HTHH, THHH<BR>\n" );
document.write( "6 outcomes of HHTT<BR>\n" );
document.write( "4 outcomes of HTTT <BR>\n" );
document.write( "1 outcome of TTTT\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And questions will be of the form \"find the probability of getting 2 or more heads\" or \"find the probability of getting more than 1 tail\" etc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "More than 2 tails are:<BR>\n" );
document.write( "HTTT<BR>\n" );
document.write( "THTT<BR>\n" );
document.write( "TTHT<BR>\n" );
document.write( "TTTH\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "TTTT\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );