YES, THAT USUALLY HAPPENS: I know they're doing this in frenzied fashion, but CNN's online editor really fell asleep at the switch for this one:

A suicide bomber set off a massive explosion Thursday in the heart of downtown Jerusalem, police said, killing at least two people and wounding more than 50.
Police said they believed the bomber was also killed.

Let's see... if a "suicide bomber" sets off a "massive explosion," yes, the bomber would usually be killed. The word "suicide" is there for a reason.