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MATH / A European train compartment has six seats. Four of the seats are broken.…

Problem

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

problem

A European train compartment has six seats. Four of the seats are broken. Wilhelm needs to fill out a form like the one here to indicate that there are broken seats. If he randomly checks off four of the seats in the diagram, what is the probability that he marked the correct seats? Express your answer as a common fraction. [asy] draw((0,0)--(24,0)--(24,18)--(0,18)--(0,0)); label("$\textbf{Maintenance Report}$",(12,16)); draw((2,2)--(22,2)--(22,14)--(2,14)--(2,2)); draw((4,4)--(8,4)--(8,6)--(4,6)--(4,4)); draw((10,4)--(14,4)--(14,6)--(10,6)--(10,4)); label("$\surd$",(12,5)); draw((16,4)--(20,4)--(20,6)--(16,6)--(16,4)); label("$\surd$",(18,5)); draw((4,10)--(8,10)--(8,12)--(4,12)--(4,10)); label("$\surd$",(6,11)); draw((10,10)--(14,10)--(14,12)--(10,12)--(10,10)); label("$\surd$",(12,11)); draw((16,10)--(20,10)--(20,12)--(16,12)--(16,10)); [/asy]
Plain-text mathematical notation (without MathML)
A European train compartment has six seats.  Four of the seats are broken.  Wilhelm needs to fill out a form like the one here to indicate that there are broken seats.  If he randomly checks off four of the seats in the diagram, what is the probability that he marked the correct seats?  Express your answer as a common fraction.

[asy]

draw((0,0)--(24,0)--(24,18)--(0,18)--(0,0));

label("$\textbf{Maintenance Report}$",(12,16));

draw((2,2)--(22,2)--(22,14)--(2,14)--(2,2));

draw((4,4)--(8,4)--(8,6)--(4,6)--(4,4));

draw((10,4)--(14,4)--(14,6)--(10,6)--(10,4));
label("$\surd$",(12,5));

draw((16,4)--(20,4)--(20,6)--(16,6)--(16,4));
label("$\surd$",(18,5));

draw((4,10)--(8,10)--(8,12)--(4,12)--(4,10));
label("$\surd$",(6,11));

draw((10,10)--(14,10)--(14,12)--(10,12)--(10,10));
label("$\surd$",(12,11));

draw((16,10)--(20,10)--(20,12)--(16,12)--(16,10));

[/asy]
Original LaTeX notation
A European train compartment has six seats.  Four of the seats are broken.  Wilhelm needs to fill out a form like the one here to indicate that there are broken seats.  If he randomly checks off four of the seats in the diagram, what is the probability that he marked the correct seats?  Express your answer as a common fraction.

[asy]

draw((0,0)--(24,0)--(24,18)--(0,18)--(0,0));

label("$\textbf{Maintenance Report}$",(12,16));

draw((2,2)--(22,2)--(22,14)--(2,14)--(2,2));

draw((4,4)--(8,4)--(8,6)--(4,6)--(4,4));

draw((10,4)--(14,4)--(14,6)--(10,6)--(10,4));
label("$\surd$",(12,5));

draw((16,4)--(20,4)--(20,6)--(16,6)--(16,4));
label("$\surd$",(18,5));

draw((4,10)--(8,10)--(8,12)--(4,12)--(4,10));
label("$\surd$",(6,11));

draw((10,10)--(14,10)--(14,12)--(10,12)--(10,10));
label("$\surd$",(12,11));

draw((16,10)--(20,10)--(20,12)--(16,12)--(16,10));

[/asy]

level

Level 3

type

Counting & Probability

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Source and history

task_id
a6fbc406-2f6f-5281-93e2-720c649d49cb
task_key
counting~5fand~5fprobability--test--a6fbc406-2f6f-5281-93e2-720c649d49cb
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import