document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=313330>Question 313330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the probability of NOT tossing 3 heads with 3 fair coins? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224061 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=224061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It would be 1 minus the probability of tossing 3 heads with 3 fair coins.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability of getting a head on one toss is equal to 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability of getting a tail on one toss is equal to 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability of tossing 3 heads with 3 fair coins is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1/2 * 1/2 * 1/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That probability becomes 1/8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability of NOT tossing 3 heads would then be 1 - 1/8 = 7/8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That probability can also be determined the hard way as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you don't toss 3 heads in a row, then you can toss:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0 heads out of 3 tosses, or 1 head out of 3 tosses, or 2 heads out of 3 tosses.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability of tossing 0 heads out of 3 tosses is the same as the probability of tossing 3 heads out of 3 tosses.   That equals 1/8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability of tossing 1 head out of 3 tosses is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1/2 * 1/2 * 1/2 * 3 = 1/8 * 3 = 3/8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This itself is the probability of tossing:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "htt or tht or tth\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since tossing 1 head out of 3 tosses can happen in 3 ways, and the probability for each of those ways is the same, you need to multiply the probability by 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability of htt is 1/2 * 1/2 * 1/2 = 1/8<BR>\n" );
document.write( "The probability of tht is 1/2 * 1/2 * 1/2 = 1/8<BR>\n" );
document.write( "the probability of tth is 1/2 * 1/2 * 1/2 = 1/8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability of tossing 2 heads out of 3 tosses becomes 3/8 as well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "hht = 1/2 * 1/2 * 1/2 = 1/8<BR>\n" );
document.write( "hth = 1/2 * 1/2 * 1/2 = 1/8<BR>\n" );
document.write( "thh = 1/2 * 1/2 * 1/2 = 1/8\r<BR>\n" );
document.write( "\n" );
document.write( "Total is 3/8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability of not getting 3 heads in 3 tosses is therefore.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(0 heads) = 1/8<BR>\n" );
document.write( "p(1 head) = 3/8<BR>\n" );
document.write( "p(2 heads) = 3/8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Total probability of p(0 or 1 or 2) = p(0) + p(1) + p(2) = 1/8 + 2/8 + 3/8 = 7/8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The easy way was to take 1 minus the probability of 3 heads which we did up top.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You get the same answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );