Although questions with 吧 and 吗 both indicate that the speaker has made an assumption of the situation and has an expectation as to what the answer will be, 吧 shows a stronger assumption or expectation than 吗.
(Situation: Someone has bought several French textbooks and two French dictionaries at a bookshop. The cashier could ask any of the following:)
你是学法文的吧?
Nǐ shì xué fǎ wén de ba ?
You must be studying French, aren’t you?
你是学法文的吗？
Nǐ shì xué fǎ wén de ma ?
Are you studying French?
你是不是学法文的？
Nǐ shì bú shì xué fǎ wén de？
Are you (or are you not) studying French?
[1] Yip, P. C., Rimmington, D., Xiaoming, Z., & Henson, R. (2009). Basic Chinese: a grammar and workbook. Taylor & Francis.
[2] Teng, W. H. (2016). Yufa! A practical guide to Mandarin Chinese grammar. Taylor & Francis.
