document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70812>Question 70812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Our country has had 43 presidents.   Write each president's last name  on a card and place all 43 cards in a box.   Note that several names ( e.g.,  Cleveland) occur twice.   Now, randomly select 2 cards from the box.<BR>\n" );
document.write( "What's the probability that the 2 names begin with the same letter?\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "1. G. Washington<BR>\n" );
document.write( "2. J. Adams<BR>\n" );
document.write( "3. T. Jefferson<BR>\n" );
document.write( "4. J. Madison<BR>\n" );
document.write( "5. J. Monroe<BR>\n" );
document.write( "6. J.Q. Adams<BR>\n" );
document.write( "7. A. Jackson<BR>\n" );
document.write( "8. M. Van Buren<BR>\n" );
document.write( "9. W. H. Harrison<BR>\n" );
document.write( "10. J. Tyler<BR>\n" );
document.write( "11. J. Polk<BR>\n" );
document.write( "12. Z. Taylor<BR>\n" );
document.write( "13. M. Fillmore<BR>\n" );
document.write( "14. F. Pierce<BR>\n" );
document.write( "15. J. Buchanan 	<BR>\n" );
document.write( "16. A. Lincoln<BR>\n" );
document.write( "17. A. Johnson<BR>\n" );
document.write( "18. U.S. Grant<BR>\n" );
document.write( "19. R. Hayes<BR>\n" );
document.write( "20. J. Garfield<BR>\n" );
document.write( "21. C. Arthur<BR>\n" );
document.write( "22. G. Cleveland<BR>\n" );
document.write( "23. B. Harrison<BR>\n" );
document.write( "24. G. Cleveland<BR>\n" );
document.write( "25. W. McKinley<BR>\n" );
document.write( "26. T. Roosevelt<BR>\n" );
document.write( "27. W. Taft<BR>\n" );
document.write( "28. W. Wilson<BR>\n" );
document.write( "29. W. Harding<BR>\n" );
document.write( "30. C. Coolidge 	<BR>\n" );
document.write( "31. H. Hoover<BR>\n" );
document.write( "32. F.D. Roosevelt<BR>\n" );
document.write( "33. H. Truman<BR>\n" );
document.write( "34. D. Eisenhower<BR>\n" );
document.write( "35. J. F. Kennedy<BR>\n" );
document.write( "36. L.B. Johnson<BR>\n" );
document.write( "37. R. Nixon<BR>\n" );
document.write( "38. G. Ford<BR>\n" );
document.write( "39. J. Carter<BR>\n" );
document.write( "40. R. Reagan<BR>\n" );
document.write( "41. G.H.W. Bush<BR>\n" );
document.write( "42. B. Clinton<BR>\n" );
document.write( "43. G.W. Bush<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50625 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=50625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is how you should proceed.<BR>\n" );
document.write( "Develop a count of the number of last names that start<BR>\n" );
document.write( "with A, then B, then C, etc.<BR>\n" );
document.write( "Then find<BR>\n" );
document.write( "Prob(A and A) = P(A)*P(A|A)<BR>\n" );
document.write( "Prob(B and B) = P(B)*P(B|B)<BR>\n" );
document.write( "etc<BR>\n" );
document.write( "Then add up all the probabilities to get the answer you want.\r<BR>\n" );
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document.write( "---------------<BR>\n" );
document.write( "For example.<BR>\n" );
document.write( "There are three names that start with A: Adams, Adams, Arther<BR>\n" );
document.write( "Prob(A and A) = (3/43)(2/42)= 0.003<BR>\n" );
document.write( "Some are going to be zero like P(Z and Z)<BR>\n" );
document.write( "All those letters that have less than two names will be zero.<BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );