die Chance
opportunity
A favorable occasion or possibility to achieve a particular goal or experience something positive.
Das ist deine große Chance, dich zu beweisen.
This is your big opportunity to prove yourself.

chance / opportunity
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opportunity
A favorable occasion or possibility to achieve a particular goal or experience something positive.
Das ist deine große Chance, dich zu beweisen.
This is your big opportunity to prove yourself.

When 'Chance' (chance/opportunity) is followed by a noun that describes the goal or success, the preposition 'auf' is used with the accusative.
Mit dieser Ausbildung hat sie gute Chancen auf einen besseren Job.
With this training, she has good chances of getting a better job.
'Chance' (opportunity) is very often combined with an infinitive clause with 'zu'. This structure describes what the opportunity consists of.
Er hat jetzt die Chance, seinen Traum zu verwirklichen.
He now has the opportunity to make his dream come true.
When 'Chance' means an opportunity, it is often combined with active verbs such as 'nutzen' (to use), 'ergreifen' (to seize), 'bekommen' (to get), or 'verpassen' (to miss).
Das war eine einmalige Gelegenheit, und er hat die Chance sofort ergriffen.
It was a once-in-a-lifetime opportunity, and he seized the chance immediately.
To express probability, 'Chance' (chance) is often used in the plural and in fixed expressions. Typical examples are 'die Chancen stehen gut/schlecht' (the chances are good/bad) or 'sich Chancen ausrechnen' (to think one has a chance).
Gegen diesen starken Gegner rechnen sich die Spieler nur geringe Chancen aus.
Against this strong opponent, the players think they have only slim chances.
possibility
'Möglichkeit' and 'Chance' can both describe an opportunity to do something. 'Möglichkeit' is more neutral and broader: it can simply be one option among several. 'Chance' sounds more positive and often has to do with success or a good outcome. For example, you say 'eine Chance bekommen' (to get a chance) when someone can achieve something. Learners may confuse the words because they fit similarly in some sentences. When it is only about a choice or option, 'Möglichkeit' is more natural. When it is about success or a favorable opportunity, 'Chance' fits better.

Frau Lange hat im neuen Team eine gute Chance, viel Erfahrung zu sammeln.
In the new team, Ms. Lange has a good opportunity to gain a lot of experience.
In diesem Kurs gibt es die Möglichkeit, jeden Freitag Fragen zu stellen.
In this course, there is an opportunity to ask questions every Friday.