Answer to Question #122931 in Statistics and Probability for Shannon Carney

Question

Explain in your own words the statement at the bottom of page 63: "the probability that X is exactly 0.5 (or exactly anything) is precisely 0." Make sure your explanation reconciles the following:
Doesn't the pointer need to land somewhere?
Have you used the words "discrete" or "continuous" in your answer? Have you referred back to the definition of the word "continuous"?
Make sure you use the notion of infinite precision. Don't confuse precision with accuracy. Precision is a number of decimal places.
How would this scenario change if there were pegs on the edge of the circle, like the Wheel-of-Fortune wheel shown below?

Answer 1

"the probability that X is exactly 0.5 is precisely 0  - it happens almost never if it has a probability of zero. The “almost” is there precisely to acknowledge the fact that, in infinite sample spaces, 0 doesn’t imply impossibility. A continuous distribution describes the probabilities of the possible values of a continuous random variable. A continuous random variable is a random variable with a set of possible values (known as the range) that is infinite and uncountable. It is not a discrete random variable , because with a discrete probability distribution, each possible value of the discrete random variable can be associated with a non-zero probability