You are playing a variant of the “cups and balls” game in which there are five cups, all face down, and there is a ball

[answerhappygod]

You are playing a variant of the “cups and balls” game in which
there are five cups, all face down, and there is a ball hidden
underneath one of the five cups. The handler shuffles the cups
around, and if you can guess which cup the ball is hidden under,
then you win.
You have no idea which of the five cups the ball is under, so
you make a random guess.
The handler then flips over one of the remaining four cups,
revealing that it is empty (i.e. no ball under this cup). You are
then given the option to switch your choice to one of the remaining
three cups or to stick with your original cup.
(a) What is the probability of winning if you do not switch your
choice to one of the remaining three cups?
(b) What is the probability of winning if you switch your choice
to one of the remaining three cups?
c) If you want to maximize your chances of winning, what should
you do: switch cups, or
stick with your original choice? Or does it not matter?