What is the probability of a continuous random variable assuming a particular value?

The probability of a continuous random variable assuming a particular value is always 0. This is because continuous random variables can take an infinite number of possible values within a given interval. When considering the probability of selecting exactly one specific value, there are infinitely many other values that could also occur in a very small range around it, making the likelihood of selecting just that one value negligible.

In continuous probability distributions, we are more interested in the probability of the variable falling within a range of values, rather than taking on any single specific value. For example, while it is accurate to discuss the probability of a random variable falling between two points (which can be calculated and is greater than 0), the probability of it being exactly equal to a specific point is universally defined as 0. Consequently, the correct answer reflects this fundamental property of continuous random variables.