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2009 AMC 8 Problems/Problem 12: Difference between revisions

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The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?
The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?


<asy>unitsize(30);  
<asy>
unitsize(30);  
draw(unitcircle);
draw(unitcircle);
draw((0,0)--(0,-1));
draw((0,0)--(0,-1));
Line 9: Line 10:
label("$1$",(0,.5));
label("$1$",(0,.5));
label("$3$",((cos(pi/6))/2,(-sin(pi/6))/2));
label("$3$",((cos(pi/6))/2,(-sin(pi/6))/2));
label("$5$",(-(cos(pi/6))/2,(-sin(pi/6))/2));[/asy]
label("$5$",(-(cos(pi/6))/2,(-sin(pi/6))/2));</asy>
[asy]unitsize(30);
draw(unitcircle);
draw((0,0)--(0,-1));
draw((0,0)--(cos(pi/6),sin(pi/6)));
draw((0,0)--(-cos(pi/6),sin(pi/6)));
label("$2$",(0,.5));
label("$4$",((cos(pi/6))/2,(-sin(pi/6))/2));
label("$6$",(-(cos(pi/6))/2,(-sin(pi/6))/2));</asy>
<math> \textbf{(A)}\ \frac {1}{2} \qquad \textbf{(B)}\ \frac {2}{3} \qquad \textbf{(C)}\ \frac {3}{4} \qquad \textbf{(D)}\ \frac {7}{9} \qquad \textbf{(E)}\ \frac {5}{6}</math>
<math> \textbf{(A)}\ \frac {1}{2} \qquad \textbf{(B)}\ \frac {2}{3} \qquad \textbf{(C)}\ \frac {3}{4} \qquad \textbf{(D)}\ \frac {7}{9} \qquad \textbf{(E)}\ \frac {5}{6}</math>

Revision as of 12:25, 14 August 2011

Problem

The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?

[asy] unitsize(30); draw(unitcircle); draw((0,0)--(0,-1)); draw((0,0)--(cos(pi/6),sin(pi/6))); draw((0,0)--(-cos(pi/6),sin(pi/6))); label("$1$",(0,.5)); label("$3$",((cos(pi/6))/2,(-sin(pi/6))/2)); label("$5$",(-(cos(pi/6))/2,(-sin(pi/6))/2));[/asy] $\textbf{(A)}\ \frac {1}{2} \qquad \textbf{(B)}\ \frac {2}{3} \qquad \textbf{(C)}\ \frac {3}{4} \qquad \textbf{(D)}\ \frac {7}{9} \qquad \textbf{(E)}\ \frac {5}{6}$

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