1. If I happened to win the lottery, I would travel around the world. Second conditional: low degree of probability. You think this is unlikely. NB note the correction: 'happened' not 'happen'. 2. If I happen to win the lottery, I will travel around the world. First conditional: relatively high degree of probability.

I agree with the others that the sentence with “would” makes more sense, as winning the lottery is rather unlikely. However, that sentence (sentence number 1) has a mistake — it should be “if I happened to win the lottery, I would….” In the spoken language, the -ed would be inaudible, but we definitely need to write it. Sentence 2, on the other hand is grammatically correct, although it suggests a relatively high probability of winning.

Number one is correct.

Well actually this is a question in my English test: "If I happen to win the lottery, I ____travel around the world. A. would B. will I thought B was the correct answer because it is grammatically correct. But then I reconsidered and chose A because winning the lottery is something nearly improbable. That decision prevented me from receiving a full score in my test!! Anyway, thanks to your answers, I have understood why "will" is correct; however, I really think there is a problem with this question.

Number two is correct. Number one would be correct if it said "If I happened to win the lottery, I would travel around the world. But both neither sound natural. This is better: 1. If I won the lottery, I would travel around the world. 2. I win the lottery, I will travel around the world.