probability

Problem 5 (5 points) Suppose in a game, a player rst chooses a number between 1 and 6 and writes down this number on a notebook. Three fair dice are then rolled. If the player's number does not appear, the player does not win any money. However, if the number does appear, the player wins $1 for each appearance. For example, suppose the player chooses 5. If the dice land 5-5-5, the player wins $3. If the dice land 545, the player wins $2. If the dice land 265, the player wins $1. If the dice land 123, the player wins $0. Suppose the game is played 100 times, and let X be the total amount of money that the player wins (in dollars). Write down the probability mass function (pmf) of X and state your reasoning