Bitcoin address security

Question

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?

Answer 1

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.