When I'm watching SpaceX launches, my biggest concern is to avoid a big boom. Specifically, an explosion that would threaten the astronauts who will eventually ride the Falcon 9.
So around stage separation, I often find myself wondering how much I can relax now that the first stage is done?
It's easy to find examples of first stage failures. Most of the stories people tell result from first stage issues. But it's hard to find examples of second stage failures, especially filtering for ones that could harm a passenger, not just "failure to achieve specified orbit".
I'm looking for some kind of numbers or sense of the failure rate of first stages compared to later stages. At least some historical examples? Is my perception correct that the first stage is the most dangerous?