document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=226299>Question 226299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bob and Alice are playing Texas Hold 'Em. Bob is dealt cards 1 and 3 while Alice is dealt cards 2 and 4. Three of the five community cards are dealt (5of clubs, 6 of clubs, K of hearts). Bob has the 2 of clubs and 4of clubs.\r<BR>\n" );
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document.write( "a. What is probability that bob has a flush?<BR>\n" );
document.write( "b. What is probability that bob has a straight?<BR>\n" );
document.write( "c. What is probability of a straight flush?\r<BR>\n" );
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document.write( "Work:<BR>\n" );
document.write( "a. Is it 25% because the next cards could be one of four choices?<BR>\n" );
document.write( "b. Is the answer .5% because odds of an Ace is 1 out of 13 multiplied by odds of a 7 (1 out of 13)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #168577 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=168577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 52-5=47 cards left to choose from since you don't know Alice's cards.<BR>\n" );
document.write( "a)<BR>\n" );
document.write( "13-4=9 remaining clubs<BR>\n" );
document.write( "(9C1*38C1+9C2)/(47C2)<BR>\n" );
document.write( "=(9*38+36)/1081 The number of possible combinations of 47 cards drawn 2 at a time is 1081.<BR>\n" );
document.write( "=(342+36)/1018<BR>\n" );
document.write( "=.350... probability of a flush in the next 2 cards.<BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "there are 4 threes that will make a straight.<BR>\n" );
document.write( "(4C1*43C1 +4C2)/47C2 [combination of 1 three out of 4, times the combination of 1 of the other 43 cards, plus the combination of 2 of the threes, divided by 1018.<BR>\n" );
document.write( "=(4*43 +6)/1081<BR>\n" );
document.write( "=178/1081<BR>\n" );
document.write( "=.165... probability of a straight in the next 2 cards.<BR>\n" );
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document.write( "c)<BR>\n" );
document.write( "Only 1 card will make a straight flush, 3 of clubs.<BR>\n" );
document.write( "(1C1*46C1)/47C2 <BR>\n" );
document.write( "=46/1081<BR>\n" );
document.write( "=.0426... Probability of a straight flush in the next 2 cards.<BR>\n" );
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document.write( "Ed </SPAN>\n" );
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