document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=940217>Question 940217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help ! One enterprising gambler decides to take a bet that if he flips a coin 7 times in a row and rolls a die 7 times in a row, he will get exactly 3 heads or 2 sixes. What are his odds of winning the bet ? (answer to the nearest hundredth percent ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #573010 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=573010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "flips (fair) coin 7 times.<BR>\n" );
document.write( "rolls (fair) die 7 times.<BR>\n" );
document.write( "Find <BR>\n" );
document.write( "Probability of getting 3 heads or 2 sixes or both.\r<BR>\n" );
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document.write( "Using binomial distribution, <BR>\n" );
document.write( "For coin, p=0.5, n=7, r=3, C(n,r)=n!/((n-r)!r!)<BR>\n" );
document.write( "P(3H) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%287%2C3%29%2A0.5%5E3%2A0.5%5E%287-3%29+=+0.27344+ ALIGN=MIDDLE  ALT=\"C%287%2C3%29%2A0.5%5E3%2A0.5%5E%287-3%29+=+0.27344+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For die, p=1/6, n=7, r=2, <BR>\n" );
document.write( "P(2-\"6\")  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%287%2C2%29%2A%281%2F6%29%5E2%2A%285%2F6%29%5E5+=+0.23443+ ALIGN=MIDDLE  ALT=\"C%287%2C2%29%2A%281%2F6%29%5E2%2A%285%2F6%29%5E5+=+0.23443+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "Since the two processes can be considered independent, so P(A & B)=P(A)*P(B),<BR>\n" );
document.write( "Using<BR>\n" );
document.write( "P(A or B) = P(A) + P(B) -P(A & B)<BR>\n" );
document.write( "= 0.27344+0.23443-(0.27344*0.23443)<BR>\n" );
document.write( "= 0.4438 </SPAN>\n" );
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