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Using experience countably here is not the usual approach, Tamara. It sounds odd to me. I have (had) experience riding a horse is the expected. It seems to require a more forceful enumeration: I have only one experience riding a horse-- and it was an unpleasant one.
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‘I have had’ - yes, sorry, that’s my fault, I actually intended to write had, not got.
Alan, to me (with my Russian background) in riding horse would sound more natural.
Will it be an error if I use preposition in with experienced or it’s also acceptable?
Also, can I say something like ‘numerous experiences’ (or how to say that I have had lot’s of cases (countably) to become experienced (in) doing something?
I think it’s important to distinguish between experience meaning acquired knowledge, which is uncountable and experience meaning encounter with (not the best word but I hope you know what I mean), which is countable.
So, you would use experience (uncountable) as in a job application: I have had a lot of experience in the field of public relations.
You would also use experience (countable):
It was a unique experience for me when I first saw the leaning tower of Pisa