Which of the following random variable that take on only a countable number of possibilities?

Discrete
Non Discrete
Continuous
All of the mentioned

The correct answer is A. Discrete.

A discrete random variable is a random variable that can take on only a countable number of values. For example, the number of heads in 10 coin flips is a discrete random variable, because it can only take on the values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10.

A non-discrete random variable is a random variable that can take on an uncountable number of values. For example, the height of a person is a non-discrete random variable, because it can take on any value between 0 and infinity.

A continuous random variable is a special type of non-discrete random variable. A continuous random variable is a random variable that can take on any value within a given interval. For example, the temperature in a room is a continuous random variable, because it can take on any value between the freezing point and the boiling point of water.

I hope this helps!