SOLUTION: 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,

Question 70812: 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.
What's the probability that the 2 names begin with the same letter?

1. G. Washington
2. J. Adams
3. T. Jefferson
4. J. Madison
5. J. Monroe
6. J.Q. Adams
7. A. Jackson
8. M. Van Buren
9. W. H. Harrison
10. J. Tyler
11. J. Polk
12. Z. Taylor
13. M. Fillmore
14. F. Pierce
15. J. Buchanan
16. A. Lincoln
17. A. Johnson
18. U.S. Grant
19. R. Hayes
20. J. Garfield
21. C. Arthur
22. G. Cleveland
23. B. Harrison
24. G. Cleveland
25. W. McKinley
26. T. Roosevelt
27. W. Taft
28. W. Wilson
29. W. Harding
30. C. Coolidge
31. H. Hoover
32. F.D. Roosevelt
33. H. Truman
34. D. Eisenhower
35. J. F. Kennedy
36. L.B. Johnson
37. R. Nixon
38. G. Ford
39. J. Carter
40. R. Reagan
41. G.H.W. Bush
42. B. Clinton
43. G.W. Bush

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
This is how you should proceed.
Develop a count of the number of last names that start
with A, then B, then C, etc.
Then find
Prob(A and A) = P(A)*P(A|A)
Prob(B and B) = P(B)*P(B|B)
etc
Then add up all the probabilities to get the answer you want.
---------------
For example.
There are three names that start with A: Adams, Adams, Arther
Prob(A and A) = (3/43)(2/42)= 0.003
Some are going to be zero like P(Z and Z)
All those letters that have less than two names will be zero.
Hope this helps.
Cheers,
Stan H.
RELATED QUESTIONS
The mean age of the 43 presidents of the United States (as of 2011) on the day of... (answered by stanbon)

The mean age of the 43 presidents of the United States (as of 2011) on the day of... (answered by ewatrrr)

There are six different cards (three red and three blue) with the letters R, S, M on... (answered by ikleyn)

The engines on the Great Eastern Railway all have six axles and the cars (tankers and... (answered by Theo)

Determine which, if any, of the three statements are equivalent. a) If Fido is our dog�s (answered by solver91311)

Thirteen playing cards, ace through king, are placed randomly with faces down on a table. (answered by edjones)

The following project uses the game of Guess Your Card. This is a game in which each... (answered by solver91311)

Find the sample space S and the corresponding size n(S) for each of the random... (answered by ikleyn)

In a survey, 11 people were asked how much they spent on their child's last birthday... (answered by Theo)