Is the word provavelmente the same in Brazilian and European Portuguese?

Yes

The only difference between the word "provavelmente" in Brazilian Portuguese and Continental Portuguese is pronunciation.

In Brazilian Portuguese, the pronunciation is more "open." The vowels are pronounced clearly, and the rhythm of the word is more melodic. The unstressed syllables are more audible.

In Continental Portuguese, the pronunciation involves significant "vowel reduction." The unstressed vowels (specifically the "e" in the middle of the word) are often swallowed or pronounced as a very faint, neutralized sound (a schwa). Additionally, the "r" sound in Portugal is typically more uvular (produced further back in the throat) compared to the more retroflex or tapped "r" used in most of Brazil.

Brazilian Portuguese Examples

1. Ele provavelmente vai chegar atrasado. (He will probably arrive late.)
2. Nós provavelmente vamos viajar nas férias. (We will probably travel during the holidays.)
   3. Eu provavelmente vou esquecer o nome dela. (I will probably forget her name.)
3. Eles provavelmente estão no shopping. (They are probably at the mall.)
4. Você provavelmente vai gostar desse filme. (You will probably like this movie.)

Continental Portuguese Examples

1. Ele provavelmente chegará atrasado. (He will probably arrive late.)
2. Nós provavelmente iremos viajar nas férias. (We will probably travel during the holidays.)
3. Eu provavelmente me esquecerei do nome dela. (I will probably forget her name.)
4. Eles estão provavelmente no centro comercial. (They are probably at the shopping mall.)
5. Tu provavelmente vais gostar deste filme. (You will probably like this movie.)