Something like the trolley problem is at work here, but you're the one tied up on the tracks.

Suppose the accident rate for regular cars were 1 fatality every 100 million miles driven (it actually is in the US).

Suppose further a hypothetical self-driving car has a proven rate of 1 fatality every 1 billion miles (10x better). Except when that fatality happens, it is because the car suddenly incinerates when arriving otherwise safely at its destination. Something about the advanced AI technology makes this outcome completely random and completely unfixable.

Which do you choose? Drive yourself, 10x more dangerous? Or leave it entirely up to chance, but 10x safer?

The rational choice is to pick the self-driving car. Yet I suspect many people (including me, I admit) would choose to drive themselves.

How far apart do those numbers need to be before most people give up the steering wheel?