A gambling game works as follows: you flip a fair coin four times (one after another). You will be paid $4 if you get 0 or 1 heads and $1 if you get 3 heads. Otherwise, you have to pay $2.50.

a) Write down the sample space showing all the possible outcomes (for example, one possible outcome is (HHHH)).

b) What is the probability of winning money from this game?

c) Construct the probability distribution of the amount won when you play this game once. (Losing money is equivalent to winning a negative amount.)

d) How much can you expect to win if you played this game twenty times?