Final answer:
In this gambling game, the nature of the variable 'a' is a random variable.
Step-by-step explanation:
In this gambling game, the random variable 'a' represents the amount of money a player can win in the game. The nature of 'a' in this scenario is (C) Random variable. A random variable is a variable that takes on different values based on the outcome of a random event, in this case, winning the game. The probability of winning a certain amount of money is given by 1/2^k, where k is the amount of money the player can win minus 2.