Add sync of default phone calendar with Google calendar

Hi - if there is anyone out there who can solve this small calendar problem I would be eternally grateful.

Currently my phone can display both its internal calendar and my Google calendar (which naturally syncs with the one on-line).

If I add an event, the default is always to add it to the built-in calendar, which doesn't sync with the google calendar. There appears to be no way to change this.

At present, I have the annoying problem of having to always remember to select 'Google calendar' when adding an event.

The solution could be:

1. Getting the built-in calendar to sync with Google calendar
OR - 2. Allowing the Google calendar to be the default choice when adding an event

Maybe option 2 would be easier? However both are beyond my ability!

Cheers,

R