No one will be able to guess the 12 words you've generated realistically. There's more chances for you to win the lottery a dozen of times on a row, than guess someone else's seed.

I wonder, though. Even if you didn't get the above answer, wouldn't it alert you to use a passphrase if having *just* the seed wasn't secure enough?

Alright, let's calculate it. The mnemonic that is given to you is a representation of a 128-bit entropy to words. So, in order for someone to generate exactly the same phrase with you, they'd have 1 in 2¹²⁸ chances.

To make this look huge, I'll write it decimally:

Note that generating a seed and deriving its addresses (to check if they're funded) isn't a procedure similar to counting. It requires much more computational power to calculate the seed of a number. There are hash functions involved such as HMAC-512, which will slow down the process.

If we assume that there's a strange person who wants to brute force the entire 128-bit range, then yeah. It'll be much harder.