Which of these is a common feature for the lac and trp operon?
regulatory proteins bind to operator
regulatory proteins bind to promoter
regulatory proteins bind to repressor

Regulatory proteins bind to repressor 

trp operon and lac operon are two different systems: trp operon is repressible while lac operon is inducible. Their common feature is that both have effector molecules that binds with repressor proteins, but the interactions yield different results. In an inducible system like lac operon, the interaction was initiated so that the repressor protein cannot bind to the operator, while in a repressible system like trp operon, the interaction was made so that the repressor protein can bind to the operator.

Yes he thought they should be left to chance why, because he thought that was the best thing to do