Rule of a game is as follow:
1. Player chooses any number on a dice (1 to 6).
2. Banker throws 3 dice. If there are n (1,2 or 3) dice showing the same number chosen by the player, banker will pay n coins to the player, otherwise, player will pay 1 coin to the banker.
If X = No. of coins won by the player, then the probability distribution of X is a binomial distribution. Is this true? If yes, please explain.