document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278057>Question 278057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What are the odds against drawing a club and a diamond? \r<BR>\n" );
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document.write( "What are the odds against getting all heads  or all tails in three successive flips of a coin? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202376 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=202376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What are the odds against drawing a club and a diamond?<BR>\n" );
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document.write( "To get the odds against you need the probability for and the probability<BR>\n" );
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document.write( "P(club and diamond) = (13/52)(13/51) <BR>\n" );
document.write( "P(not drawing a club and a diamond) = 1 - (13^2/(52*51)) = (52*51-13^2)/(52*51)<BR>\n" );
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document.write( "Then odds against = P(against)/P(for) = (52*51-13^2)/13^2 = 2483:169<BR>\n" );
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document.write( "What are the odds against getting all heads or all tails in three successive flips of a coin?<BR>\n" );
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document.write( "P(all heads) = 1/8<BR>\n" );
document.write( "P(all tails) = 1/8<BR>\n" );
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document.write( "Assuming these events are independent you get:<BR>\n" );
document.write( "P(all heads and all tails) = (1/8)^2 = 1/64<BR>\n" );
document.write( "P(not) = 1-(1/64) = 63/64<BR>\n" );
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document.write( "Then odd against = P(not)/P(for) = 63/1 = 63:1<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  <BR>\n" );
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