Question

Nicolás is a great bettor in the famous game of "rock, paper or scissors" and whenever...

Nicolás is a great bettor in the famous game of "rock, paper or scissors" and whenever he can, he tries to hunt bets with his friends. Carlos and Camila are two of them. Nicolás estimates that the next bet will be made with Carlos with a triple probability than he will do with Camila. If he faces Carlos, they will play 2 times, while if he faces Camila, they will play 3 times. In each bet, Nicolás pays $ 1.5 if he loses a game and will receive $ 1 if he wins it, regardless of whether he plays against Camila or Carlos. In all cases, Nicolás estimates that he will win each individual game with a probability of 60%. From the information above:

a. Find the probability function of the amount of money Nicolas can win or lose. Define the random variable X and the range values of the variable.

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