
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.

chance
The probability or prospect of success in an undertaking.
Die Chancen stehen gut, dass wir das Spiel gewinnen.
The chances are good that we will win the game.
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
Both words refer to an option to do something specific. „Möglichkeit“ neutrally describes the fact that an action is open to someone, while „Chance“ additionally emphasizes a favorable prospect of achieving a desired result. If you are talking only about what is possible, „Möglichkeit“ is suitable; when there is a positive prospect of success, „Chance“ is more appropriate.

Mit diesem Kurs habe ich eine gute Chance, die Prüfung noch zu bestehen.
With this course, I have a good chance of still passing the exam.
Mit diesem Kurs habe ich die Möglichkeit, die Prüfung noch zu bestehen.
With this course, I have the option of still passing the exam.