There are 100 boxes each containing a dollar bill. Every turn you open a random box and take the bill, unless the box is already empty – the bills are not replaced. You play this game for 50 turns.
(a) How likely is that a given box will be opened at least once during a game?
(b) What is your expected win?
Hint for part $b$,your earning, $X$ is equal to the number of boxes that is opened at least once.
Use part $a$ and indicator variable
Write $$X= \sum_{i=1}^{100} X_i$$
for some indicator variable, then we have $$E[X]= \sum_{i=1}^{100} E[X_i]$$