I agree with 돼 but 하요 해요 also completely confusing to me. My way of distinguishing it is to put 어 between 되 and 요 and it sounds ok 돼요 is correct. Generally 되요 is understood that become, while 돼요 is allowance. There are other examples like that which Koreans also would be very confused

Thanks for the detailed information! This is really helpful!! :) I was in Korea in May and had a great time but didn't know the language. So I'll learn it now and go back someday!

I'm afraid that she, who got your sentenced corrected below, was also confused with the use of 돼요 and 되요. Even Korean have a difficulty in using 돼 or 되 correctly. The point is that you are correct. You are corretly using 돼요. If you want to say that you are permitted to do something, admitted to do something, accepted to do something, you would be right to use "돼" not "되" I am sorry that I can't explain about it with more detail or with more grammar. Bur here's a tip of discerning the usage when you will become a little bit advanced in Korean. If you are not sure which is correct to use between 돼 and 되, just try to replace the letter in question with the letter 해 or 하 and read it loudly. For example, if you are not sure that "한국에 가도 돼요" is correct or "한국에 가도 되요" is correct, change the letter 돼 with 해, the letter 되 with 하 and read each words loudly. In this case, you will read 해요, 하요 respectively. For most Koreans, 해요 sounds OK and it appears not to have any grammatical errors, but "하요" sounds weird and awkward. So in this case 해요 is correct to use, consequently "돼요" is corret usage grammatically. I know that this explanation is not enough and even could make you more confused. But as you are learning Korean more and more, I am sure that you will have a time to get the picture of what I juse explained. I am sorry for lacking in give you more understandable explanation because of my English inability. and Thank your for having interest in Korean. ^^