Step 1: Think about vessel anatomy.
Hypertensive bleeds happen where small deep arteries take blood almost straight off a bigger vessel. That sharp branching point takes the most pressure.
Step 2: Map that anatomy to the brain.
The lenticulostriate branches of the middle cerebral artery supply the putamen, and they branch off at a near right angle. This makes the putamen the classic weak point.
Step 3: Compare with the other choices.
The cerebellum, pons and midbrain are all possible sites of hypertensive hemorrhage, but each is struck far less often than the putamen, and the pons ranks behind the thalamus in frequency.
Step 4: Settle on the answer.
Since the putamen accounts for the largest share of hypertensive bleeds, it is the correct choice.
\[ \boxed{\text{Putamen}} \]