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I understand bitcoin addresses are randomly selected from such a large pool that the statistical chances of someone discovering your address is very low.

In light of the above is it still not possible?

i.e. if I have a large holding of bitcoin in an address the someone "could" by chance generate the same private key and access my fund.

Is this correct?

marked as duplicate by Nate Eldredge, Jestin, Murch Jul 25 '16 at 6:00

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Technically, yes.
Realistically, no.

As long as your private key is random, you should be fine.

Still concerned? Maybe you want to consider multisig, as it would require M of N keys to collide, making the already practically impossible, even more impossible.

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