Why do hair professionals provide free hair coloring services to people sometimes?

For practice. They might have some trainees and offering you a free colouring is basically a way to teach them. However, there is always a danger that the hairdresser will do a bad job, but it can be a price to pay for a free new style.

Or, for publicity. If they do a good job, your friend will ask and you'll tell them. Then your friend will tell her mother who will tell her sister who will tell her cousin who will tell her daughter who will tell her teacher and so on. Lots of people will find out about it at no cost to the hair place.

I would not think they need to do it for practice, that is what beauty schools are for and they charge at beauty schools, although a reduced rate.

Maybe once in a while they will do it for charity, for women in homeless or battered shelters, but I would think it would be very mainstream color and cut to help these women.

A third thing may be some product manufacturer is trying to gain acceptance and is paying pros to try their product out on volunteers who are not paying. In this case, I would think that the volunteers have to be up for a variety of colors.

Years ago a woman approached me in a store because she needed "heads" for color/cut for a show or something. I was flattered but declined. It sounds like someone may be pressuring you and in this case I think you should say no. I think your instincts are right.

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