I wouldn't press the button, simply because it's not my job to do so.
On the topic of the button, Here's some fun thoughts for you all:
Let's assume you can press the button 3 times a second. In an hour, you can press it 10800 times. There are about 8 Billion people on the world. That'll mean you need to press the button for about 741,000 hours before everyone disappears, which is about 85 years of non-stop button pressing.
Now, let's analyse the scenario a bit more.
We have a 70% chance of a 'bad' person being picked. We have a 30% chance of an 'innocent' person being picked.
The problem? It's not a 30% chance that a random person is picked. It's a 30% chance that a person known innocent is picked.
Why is this problematic? Let's assume n% of a population is bad, and so (100-n)% is good. If n is low, (below 70%) then the button has a bias towards picking 'bad' people.
What happens as n gets higher? if n reaches 70%, then you're effectively just picking a random person to send to solitary confinement. If n gets even higher, (above 70%) then the button has a bias towards picking 'innocent' people.
So the question is, what proportion of people are 'bad' according to your standards? If you believe that over 70% of people do not fit your personal criteria for good standards, then the button's capability to judge according to those standards is worse than a random number generator.