Comme un jeu

Let \(X\) represent the net gain (in dollars) from a game where you pay \(\dollar\)2 to play and toss two fair coins: a red coin

and a blue coin

. You receive a payout of \(\dollar\)1 if no heads appear, \(\dollar\)3 if one head appears, and \(\dollar\)5 if two heads appear. Determine the value of \(X\) for each of the following outcomes:

\(X(\textcolor{colordef}{T},\textcolor{colorprop}{T}) = \)

,
\(X(\textcolor{colordef}{H},\textcolor{colorprop}{T}) = \)

,
\(X(\textcolor{colordef}{T},\textcolor{colorprop}{H}) = \)

,
\(X(\textcolor{colordef}{H},\textcolor{colorprop}{H}) = \)

.