# Random forest - OOB error rate when some observations appear in all tree

I am just curious about how Random forest calculates the (Out-of-bag) OOB error rate.

In my course note, it says that RF will predict each observation using only trees in which that observation does not appear. It makes sense but what if a observation appears in all the tree, how can we calculate OOB error rate for this observation?

Really appreciate any help

There are some excellent answers there as to why, but suffice to say that the probability of any observation being selected in any one bootstrap dataset is $\sim \frac{2}{3}$. Actually it approaches $1 - \frac{1}{e}$ for large datasets.
$\left( \frac{2}{3}\right) ^ {500} = 9\mathrm{e}{-89}$