Chance of shower, one missed by flipping ministry (6)

I believe the answer is:

random

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'chance' is the definition.
(similar in meaning)

'shower one missed by flipping ministry' is the wordplay.
'shower' becomes 'rain' (rainfall).
'one' becomes 'i' (Roman numeral).
'missed by' indicates named letters should be taken away.
'flipping ministry' becomes 'dom' (I can't justify this - if you can you should believe this answer much more).
'rain' with 'i' removed is 'ran'.
'ran'+'dom'='RANDOM'

'of' is the link.

Can you help me to learn more?

(Other definitions for random that I've seen before include "Done or taken without particular aim" , "casual?" , "Happening by chance, haphazard" , "Lacking regularity" , "Haphazard, no fixed pattern" .)

I've seen this clue in The Times.

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