A few year’s ago I used to work in Downtown LA. One day I accidentally got stuck in the wrong lane and had to exit the freeway. The next entrance for the freeway was closed for construction, so I had to follow some detours to find the next entrance. Once this happened I discovered that this route would save me some time from the usual traffic in the freeway. I estimated that this route was saving me 3-5 minutes daily. I worked at my job for another 2 years after that point and I took that route daily, which at the end saved me a lot of time.
A “prepared mind,” means to always be ready and have an open, such that when accidental discoveries happen, you realize it. A person can prepare their mind to be open to chance by knowing that many scientific findings in the past have happened by accident.
Another good example of how an accident may have benefited the humanity is the discovery of cooking food. Our prehistoric ancestors probably discovered that meat tasted much better if cooked when they ran into burned animals due to jungle fires.
I think the sciences of physics and chemistry would both be good for letting people analyze their accidents.
I have read the story of Marie Curie when I was in junior high school. In case you don’t know her story, she discovered radioactivity, but sadly she died of exposure to radioactivity, because at the time the risks were not known. That is a good example of risks associated with research. Death is probably the worst example of risks with scientific discoveries that involves chance. Other risks could involve sickness and damage to personal or laboratory property. No doubt, many scientists have probably burned their laboratories due to explosions and fires, but at the end they have probably discovered something new.