Do Protestants believe in the trinity?

Not all. According to the New Bible Dictionary: "The term 'Trinity' is not itself found in the Bible. It was first used by Tertullian at the close of the 2nd century, but received wide currency [common use in intellectual discussion] and formal elucidation [clarification] only in the 4th and 5 centuries" (1996, "Trinity").

It further explains that "the formal doctrine of the Trinity was the result of several inadequate attempts to explain who and what the Christian God is...To deal with these problems the Church Fathers met in [A.D.] 325 at the Council of Nicaea to set out an orthodox biblical definition concerning the divine identity." However, it would not be until 381 A.D. at the Council of Constantinople that the divinity of the Spirit was affirmed (ibid.).

This is a manmade concept and not found anywhere in the Bible. So many have made surprising admissions about the Trinity - "an absolute mystery," "mysterious in its origin and its content," "impossible for Christians actually to understand," " unintelligible," "misunderstood," "presents strange paradoxes" and "widely disputed." One would have to question then why/how a doctrine on which billions of people base their faith and salvation is accepted. The Apostle Paul was inspired to tell us in 1 Corinthians 14:33 that "God is not the author of confusion" yet this doctrine of men is total confusion.

Yes: all Christians believe in the Trinity of: God the Father, God the Son, and God the Holy Spirit.