por acaso & de propósito

por acaso in portuguese

por acaso » by chance

Simônimos » inesperadamente, acidentalmente, casualmente, aleatoriamente, arbitrariamente
Exemplo:

Encontrei meus primos no festival por acaso. Não tínhamos combinado nada. » I met my cousins at the festival by chance. We hadn't arranged anything.

de propósito » on purpose

Simônimos » deliberadamente, intencionalmente
Exemplo:

O propósito da vida é seguir a felicidade de propósito. » The purpose of life is to pursue happiness on purpose.

Well, these two go together pretty well, correto?

Initially I had this tagged as an advanced topic but these are really transparent and within reach of anyone at the intermediate level, com certeza!

Let's dissect:
por acaso == (literally) per chance = by chance *interesting to note that caso = case
de propósito == (literally) of purpose = on purpose

Easy peasy lemon squeezy.
Let's go straight to some real-life examples!

por acaso

» From our online Portuguese course.