An example of an idea for a new start$-$up from an accidental discovery is:

a furniture salesperson seeing the possibility of opening a new furniture store in a different area of the city

a sharpshooter, who shot holes in a pair of her boyfriend${}^{TM}s$ jeans during an argument, hearing him get complimented on the way they look

a purposeful exploration to find a new idea

a coin collector, who bought and sold coins for years to build a personal collection, deciding to become a coin dealer