Untouched Trees

In a Random Forest with bagging, each tree is trained on a bootstrap sample drawn with replacement from $n$ training examples. As $n$ grows large, roughly what fraction of the original examples is expected to be left out of any single tree's bootstrap sample (and thus usable for that tree's out-of-bag estimate)?

$\sim 63.2%$

$\sim 90%$

$\sim 36.8%$ ( $1/e$ )

$\sim 50%$

$\sim 10%$