Please answer for a,b,c,d

[8 marks] 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) [1 mark] Write down the sample space showing all the possible outcomes (for example, one possible outcome is (HHHH)). b) [2 marks] What is the probability of winning money from this game? c) [3 marks] Construct the probability distribution of the amount won when you play this game once. (Losing money is equivalent to winning a negative amount.) d) [2 marks] How much can you expect to win if you played this game twenty times