Permissions problem

Hi, sorry to have to ask for help as I've spent a long time with trial and error and checked the help forums but I just cant get this to work as desired. I'm having a problem with permissions and would like to know the correct settings for this scenario

- Public surveys (category) - should be able to be answered by anyone without logging in

- Private surveys (category) - user needs to be in Registered user group and needs to be logged in to answer

Please also confirm the component permissions settings for this scenario too.

Many thanks,

James