\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A fair six-sided die is rolled in a game where you pay \(\dollar\)3 to play and receive a payout (in dollars) equal to 2 times the number shown on the die, as shown in this example:
\(\text{Payout: } 2 \times \textcolor{colordef}{2} = 4 \text{ dollars}, \text{ Net Gain: } 4 - 3 = 1\)
The random variable \(X\) represents the net gain from the game.
Choose the one correct answer: