Difference between revisions of "1988 AHSME Problems/Problem 12"

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==Solution==
 
==Solution==
We can draw a sample space diagram, and find that of the <math>9^2 = 81</math> possibilities, <math>9</math> of them give a sum of <math>0</math>, and each other sum mod <math>10</math> (from <math>1</math> to <math>9</math>) is given by <math>8</math> of the possibilities (and indeed we can check that <math>9 + 8 \times 9 = 81</math>). Thus <math>0</math> is the most likely, so the answer is <math>A</math>.
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We can draw a sample space diagram, and find that of the <math>9^2 = 81</math> possibilities, <math>9</math> of them give a sum of <math>0</math>, and each other sum mod <math>10</math> (from <math>1</math> to <math>9</math>) is given by <math>8</math> of the possibilities (and indeed we can check that <math>9 + 8 \times 9 = 81</math>). Thus <math>0</math> is the most likely, so the answer is <math>\boxed{\text{A}}</math>.
  
  

Revision as of 17:15, 26 February 2018

Problem

Each integer $1$ through $9$ is written on a separate slip of paper and all nine slips are put into a hat. Jack picks one of these slips at random and puts it back. Then Jill picks a slip at random. Which digit is most likely to be the units digit of the sum of Jack's integer and Jill's integer?

$\textbf{(A)}\ 0\qquad \textbf{(B)}\ 1\qquad \textbf{(C)}\ 8\qquad \textbf{(D)}\ 9\qquad \textbf{(E)}\ \text{each digit is equally likely}$

Solution

We can draw a sample space diagram, and find that of the $9^2 = 81$ possibilities, $9$ of them give a sum of $0$, and each other sum mod $10$ (from $1$ to $9$) is given by $8$ of the possibilities (and indeed we can check that $9 + 8 \times 9 = 81$). Thus $0$ is the most likely, so the answer is $\boxed{\text{A}}$.


See also

1988 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

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