Maybe a mathematician can explain whether this "trick" works or not? Intuitively, I can't see that knowing whether the M&M demand was filled makes it more probable that the other demands are filled.
Say you have a pile with five black or white marbles. You want them all to be black. So you check that the first marble in the pile is black (ie no brown m&m:s). Is it now more probable that the other four marbles also are black?
Because you are just checking one specific marble instead of sampling a number of randomly chosen marbles (which of course would increase the probability), I don't see how it can work.
Say you have a pile with five black or white marbles. You want them all to be black. So you check that the first marble in the pile is black (ie no brown m&m:s). Is it now more probable that the other four marbles also are black?
Because you are just checking one specific marble instead of sampling a number of randomly chosen marbles (which of course would increase the probability), I don't see how it can work.