don't you mean chance of losing every bet?

Yes.

If so, no way in hell those are conditionally independent.

Of course they are not conditionally independent, that's why I gave it as a lower bound.

Specifically, I think we can agree that whatever the exact relationships, the failure of one bet will increase the chance of failure of all the others: if the 6-month sheep bet fails, then the 12-month becomes more likely to fail, and to a smaller degree, the BMR ones become more likely to fail. And not the other way around. Hence independence is the best-case scenario, and so it's the lower bound, and that's why I wrote ">10%".