Is mixed-race priceless? No worries! (8)

I believe the answer is:

carefree

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'is mixed-race priceless? no worries' is the definition.
I can't tell whether this defines the answer.

'is mixed-race priceless?' is the wordplay.
'is mixed' indicates an anagram.
'priceless?' becomes 'free' (I've seen this in another clue).
'race' is an anagram of 'care'.
'care'+'free'='CAREFREE'

Can you help me to learn more?

(Other definitions for carefree that I've seen before include "irresponsible" , "insouciant" , "relaxed" , "without worrying?" , "Jaunty" .)

I've seen this clue in the Sydney Morning Herald.

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