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MATH / On the game board below Kendra will start at the center of the board. For each…

Problem

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

problem

On the game board below Kendra will start at the center of the board. For each turn she will spin this spinner with four congruent sectors once, and then she will move one space in the direction indicated on the spinner. The "Start'' square does not have a numerical value, but Kendra may land on it during her turns. What is the probability that the sum of the numbers in the spaces on which she will land will be exactly 30 after her third complete turn? Express your answer as a common fraction.

[asy]size(80);
import graph;
draw(Circle((0,0),1),linewidth(1));
draw((-1,0)--(1,0),linewidth(1)); draw((0,-1)--(0,1),linewidth(1));
label("Move",(sqrt(2)/4,sqrt(2)/4+.15),fontsize(10pt));
label("Left",(sqrt(2)/4,sqrt(2)/4-.15),fontsize(10pt));
label("Move",(-sqrt(2)/4,sqrt(2)/4+.15),fontsize(10pt));
label("Right",(-sqrt(2)/4,sqrt(2)/4-.15),fontsize(10pt));
label("Move",(-sqrt(2)/4,-(sqrt(2)/4-.15)),fontsize(10pt));
label("Down",(-sqrt(2)/4,-(sqrt(2)/4+.15)),fontsize(10pt));
label("Move",(sqrt(2)/4,-(sqrt(2)/4-.15)),fontsize(10pt));
label("Up",(sqrt(2)/4,-(sqrt(2)/4+.15)),fontsize(10pt));
dot((0,0),linewidth(5)); draw((0,0)--1/2 dir(-70),linewidth(1.5),EndArrow(5));[/asy]

[asy]size(200);
picture box10,box15,box5,box20;
filldraw(box5,(-1,-.5)--(-1,.5)--(1,.5)--(1,-.5)--cycle,white,linewidth(1)); label(box5,"5",(0,0));
filldraw(box10,(-1,-.5)--(-1,.5)--(1,.5)--(1,-.5)--cycle,gray(.6),linewidth(1)); label(box10,"10",(0,0));
filldraw(box15,(-1,-.5)--(-1,.5)--(1,.5)--(1,-.5)--cycle,white,linewidth(1)); label(box15,"15",(0,0));
filldraw(box20,(-1,-.5)--(-1,.5)--(1,.5)--(1,-.5)--cycle,gray(.6),linewidth(1)); label(box20,"20",(0,0));
void b10(real x, real y)
{
add(shift(x*right)*shift(y*up)*box10);
}
void b15(real x, real y)
{
add(shift(x*right)*shift(y*up)*box15);
}
void b5(real x, real y)
{
add(shift(x*right)*shift(y*up)*box5);
}
void b20(real x, real y)
{
add(shift(x*right)*shift(y*up)*box20);
}
for(int i = 0; i<3; ++i)
{
draw((8.5-2.5i,1.5i+2)--(-8.5+2.5i,1.5i+2),linewidth(1));
draw((8.5-2.5i,-1.5i-2)--(-8.5+2.5i,-1.5i-2),linewidth(1));
}
for(int i = 0; i<3; ++i)
{
draw((8.5-2.5i,2+1.5i)--(8.5-2.5i,-2-1.5i),linewidth(1));
draw((-8.5+2.5i,2+1.5i)--(-8.5+2.5i,-2-1.5i),linewidth(1));
}
draw((8.5,0)--(-8.5,0),linewidth(1));
draw((0,5)--(0,-5),linewidth(1));
filldraw((-1,1)--(1,1)--(1,-1)--(-1,-1)--cycle,white,linewidth(1)); label("Start",(0,0),fontsize(8pt));
b10(0,2); b10(-3.5,2); b10(3.5,2); b10(-3.5,0); b10(3.5,0); b10(0,-2); b10(-3.5,-2); b10(3.5,-2); b10(3.5,5); b10(-3.5,5); b10(3.5,-5); b10(-3.5,-5);
b5(6,0); b5(8.5,0); b5(0,3.5); b5(0,5); b5(0,-3.5); b5(0,-5); b5(3.5,-3.5); b5(3.5,3.5);b5(-3.5,-3.5);b5(-3.5,3.5); b5(-6,0); b5(-8.5,0);

b20(6,3.5); b20(6,-3.5); b20(-6,3.5); b20(-6,-3.5); b20(8.5,2); b20(-8.5,2); b20(8.5,-2); b20(-8.5,-2);

b15(6,2); b15(6,-2); b15(-6,2); b15(-6,-2);[/asy]

level

Level 5

type

Counting & Probability

Discussion

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Source and history

task_id
a02ec1e5-abef-51f9-98a2-84cd334b8810
task_key
counting~5fand~5fprobability--test--a02ec1e5-abef-51f9-98a2-84cd334b8810
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import