Got it, thanks. What about if it read "but everybody changed their mind" or would it be minds?

Technically, everybody takes a singular verb. Try replacing it with "every single body" or "every person".

The main ambiquity in the phrase is that 'their' isn't -technically- correct as a gender neutral third person possessive pronoun, despite its common usage in that form. (Say -that- five times fast!) If you replace 'their' with 'his or her', the agreement makes much more sense:

    Everybody changed his or her mind.

Personally, I would just rewrite it completely:

    They all changed their minds.

English is fun!

And you can get wonderfully creative with something like

"The group changed its mind"

and

"The group changed their minds"

depending on the meaning you want the statement to have. Are you emphasizing the concept of "group-think" or the independent conclusions of the individuals?

It's more poetic than

"The members of the group changed their minds".

or

"Each group member changed his or her mind".

But at least you get a ridiculous bag of options for a single sentence.

I see, thanks!

I agree, thanks! :)

It would still be "minds", because "everybody" is referring to a plural subject. You can say "everyone put on their jackets" but not "everyone put on their jacket". The latter makes sense if the listener dismisses the absurd possibility that everyone is fitting into one jacket, but it's not correct.

While 'everyone' sounds like it refers to a plural subject, it technically is singular. Therefore, "Everyone put on their jacket." is correct. This is another one where I would rewrite the whole thing to make it sounds better:

   They all put on their jackets.