Yes, that's possible.
Happened in both the 2000 election and the 2016 election, where both times, the Democratic candidate had the popular vote, but lost the EC vote.
Whether or not it's fair is up to who you ask. Conservatives believe it's fair because the EC gives more representation to the smaller states, while Democrats believe it's unfair because people who vote against the majority in the state are not represented and because it has an inaccurate representation of the population of the United States.
