benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Two circles with spinners at their centers are divided into three equal regions…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Two circles with spinners at their centers are divided into three equal regions as shown. When both spinners are spun, what is the probability that the product of the two values is negative? Express your answer as a common fraction. [asy] size(140); void spinner(picture pic=currentpicture, real rotate, int a, int b, int c) { dot(pic,(0,0),linewidth(4)); draw(pic, unitcircle ^^ (0,0)--dir(90+rotate) ^^ (0,0)--dir(210+rotate) ^^ (0,0)--dir(-30+rotate)); label(pic, "$"+string(a)+"$",dir(30+rotate)/2,fontsize(10pt)); label(pic, "$"+string(b)+"$",dir(150+rotate)/2,fontsize(10pt)); label(pic, "$"+string(c)+"$",dir(-90+rotate)/2,fontsize(10pt)); } picture p; spinner(0,-1,-3,5); spinner(p,180,2,4,-6); draw((0,0)--dir(-10)/2,EndArrow(4)); draw(p,(0,0)--dir(-75)/2,EndArrow(4)); add(shift(2.5*right)*p);[/asy]
Plain-text mathematical notation (without MathML)
Two circles with spinners at their centers are divided into three equal regions as shown. When both spinners are spun, what is the probability that the product of the two values is negative? Express your answer as a common fraction. [asy]
size(140);
void spinner(picture pic=currentpicture, real rotate, int a, int b, int c)
{
dot(pic,(0,0),linewidth(4));
draw(pic, unitcircle ^^ (0,0)--dir(90+rotate) ^^ (0,0)--dir(210+rotate) ^^ (0,0)--dir(-30+rotate));
label(pic, "$"+string(a)+"$",dir(30+rotate)/2,fontsize(10pt));
label(pic, "$"+string(b)+"$",dir(150+rotate)/2,fontsize(10pt));
label(pic, "$"+string(c)+"$",dir(-90+rotate)/2,fontsize(10pt));
}
picture p;
spinner(0,-1,-3,5); spinner(p,180,2,4,-6);
draw((0,0)--dir(-10)/2,EndArrow(4)); draw(p,(0,0)--dir(-75)/2,EndArrow(4)); add(shift(2.5*right)*p);[/asy]
Original LaTeX notation
Two circles with spinners at their centers are divided into three equal regions as shown. When both spinners are spun, what is the probability that the product of the two values is negative? Express your answer as a common fraction. [asy]
size(140);
void spinner(picture pic=currentpicture, real rotate, int a, int b, int c)
{
dot(pic,(0,0),linewidth(4));
draw(pic, unitcircle ^^ (0,0)--dir(90+rotate) ^^ (0,0)--dir(210+rotate) ^^ (0,0)--dir(-30+rotate));
label(pic, "$"+string(a)+"$",dir(30+rotate)/2,fontsize(10pt));
label(pic, "$"+string(b)+"$",dir(150+rotate)/2,fontsize(10pt));
label(pic, "$"+string(c)+"$",dir(-90+rotate)/2,fontsize(10pt));
}
picture p;
spinner(0,-1,-3,5); spinner(p,180,2,4,-6);
draw((0,0)--dir(-10)/2,EndArrow(4)); draw(p,(0,0)--dir(-75)/2,EndArrow(4)); add(shift(2.5*right)*p);[/asy]

level

Level 2

type

Counting & Probability

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
82edac7d-5327-5b29-b042-9da5c021cfe4
task_key
counting~5fand~5fprobability--test--82edac7d-5327-5b29-b042-9da5c021cfe4
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import