Consider a game where you can pay either $2 to flip two coins, or $3 to flip three coins, and where you win a prize depending on the number of heads that show:

If three heads show, you win $7. If two heads show, you win $3. If one heads shows, you win $2. If no heads show, you don't win anything.

(a) Is it better for you to pay $2 or $3 (in terms of your expected winnings)? Justify your answer.

(b) Suppose that your friend also plays this game, but they randomly pick between paying $2 or $3 instead (so there

is a 50% probability they flip two coins, and 50% they flip three coins).

If you know that they neither won nor lost money (i.e. net winnings is $0), is it more likely that they flipped two coins or three when they played the game? Justify your answer.