Problem D

The Baseball Game

Ivy has created a game for her schoolâ€™s math fair. She put three baseballs, numbered \(1\), \(2\), and \(3\), into a bag. Without looking, a player will randomly draw a baseball from the bag, record its number, and then put the baseball back into the bag. They will do this two more times and then calculate the sum of the three numbers recorded. If the sum is less than \(8\), the player will win a prize.

What is the probability that a player will win a prize when they play this game once?