
ausfallen
to be canceled
To not take place; to be canceled.
Wegen Krankheit des Lehrers fällt der Unterricht heute aus.
Because the teacher is sick, class is canceled today.
to be canceled / to fail
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to be canceled
To not take place; to be canceled.
Wegen Krankheit des Lehrers fällt der Unterricht heute aus.
Because the teacher is sick, class is canceled today.

to fail
To stop functioning, usually because of a technical defect.
Gestern Abend ist bei uns im ganzen Viertel der Strom ausgefallen.
Yesterday evening, the power failed throughout our whole neighborhood.

to turn out
To have a certain result or a certain quality.
Die Ernte ist dieses Jahr aufgrund der Trockenheit schlecht ausgefallen.
The harvest turned out badly this year because of the drought.

to fall out
To come loose from the body and fall out, especially hair or teeth.
Seit der Krankheit fallen ihm die Haare aus.
Since the illness, his hair has been falling out.
'Ausfallen' (to be canceled / to fail) is a separable verb. The prefix 'aus-' goes at the end in main clauses; in subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Zug nach Berlin fällt heute aus.
The train to Berlin is canceled today.
The perfect tense of 'ausfallen' (to be canceled / to fail) is always formed with the auxiliary verb 'sein' (to be), because it describes a change of state. So the form is 'ist ausgefallen' (has been canceled / has failed).
Die Heizung ist mitten im Winter ausgefallen.
The heating failed in the middle of winter.
The context reveals the exact meaning. If the subject is an event or an appointment, it means 'not take place'. If the subject is a technical device or system, it means 'no longer function'.
Die morgige Vorlesung fällt aus.
Tomorrow's lecture is canceled.
In the meaning 'to have a result', 'ausfallen' (to turn out) is almost always accompanied by an adverb or adjective that describes the quality of the result.
Der Test ist besser ausgefallen als erwartet.
The test turned out better than expected.
When hair or teeth fall out, the affected person is often named with a dative object. The subject of the sentence is the thing that falls out.
Dem alten Hund fallen langsam die Zähne aus.
The old dog's teeth are slowly falling out.
to hang
When talking about technology, hängen and ausfallen both mean that something is no longer working. Hängen is often used colloquially for a frozen or blocked state. Ausfallen is especially appropriate when a device stops working completely, usually because of a technical defect.

Der Bürocomputer ist wegen eines defekten Netzteils vollständig ausgefallen.
The office computer has completely failed because of a faulty power supply.
Der Bürocomputer hängt und reagiert nicht mehr auf die Maus.
The office computer has frozen and no longer responds to the mouse.