No, you do not need a degree for most areas of the entertainment industry. People who tend to have them are executives, agents, and creative people whose parents made them go to college to have something "practical to fall back on." If you know specifically what you want to do in the entertainment industry, it is very important for you to train in your skill of choice and be up to date on all technology that applies to your craft. You also need to invest in understanding the "business side of the business." That's where I come in
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How old do you have to be? That depends on what area of the entertainment industry you want to be in. Infants and beyond can be actors. Most other classifications that pay, have labor laws that pertain to age. I'm making an assumption that you're young, so I will say, that if you have the opportunity to intern as a youth, it's a great opportunity. If you want to be more specific about what you're interested in doing, I can give you a more specific answer.