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MATH / On the number line, point A is located at 0, point B is located at 4, and point C is located at 6. [asy] defaultpen(1); draw((0,0)--(6,0)); for (int i=0;i<7;++i) draw((i,-.1)--(i,.…

Problem

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

problem

On the number line, point AA is located at 0, point BB is located at 4, and point CC is located at 6. [asy] defaultpen(1); draw((0,0)--(6,0)); for (int i=0;i<7;++i){ draw((i,-.1)--(i,.1)); label(string(i),(i,-.1),(0,-1)); } label("AA",(0,0),(0,1)); label("BB",(4,0),(0,1)); label("CC",(6,0),(0,1)); [/asy] A dart randomly lands somewhere on the number line between AA and CC. What is the probability that it lands closer to BB than it does to AA or CC?
Plain-text mathematical notation (without MathML)
On the number line, point A is located at 0, point B is located at 4, and point C is located at 6. [asy]
defaultpen(1);
draw((0,0)--(6,0));
for (int i=0;i<7;++i){

draw((i,-.1)--(i,.1));

label(string(i),(i,-.1),(0,-1));
}
label("A",(0,0),(0,1));
label("B",(4,0),(0,1));
label("C",(6,0),(0,1));
[/asy] A dart randomly lands somewhere on the number line between A and C.  What is the probability that it lands closer to B than it does to A or C?
Original LaTeX notation
On the number line, point $A$ is located at 0, point $B$ is located at 4, and point $C$ is located at 6. [asy]
defaultpen(1);
draw((0,0)--(6,0));
for (int i=0;i<7;++i){

draw((i,-.1)--(i,.1));

label(string(i),(i,-.1),(0,-1));
}
label("\(A\)",(0,0),(0,1));
label("\(B\)",(4,0),(0,1));
label("\(C\)",(6,0),(0,1));
[/asy] A dart randomly lands somewhere on the number line between $A$ and $C$.  What is the probability that it lands closer to $B$ than it does to $A$ or $C$?

level

Level 3

type

Counting & Probability

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Source and history

task_id
a99973d0-4535-5aa7-b0c8-7ad16204f0c3
task_key
counting~5fand~5fprobability--test--a99973d0-4535-5aa7-b0c8-7ad16204f0c3
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import