In the case of discrete random variables, it is quite clear that probability measure (or pmf) is quite useful since it gives the direct probability value.
But in case of a continuous random variable, in my opinion, the practicality of probability measure (valued after integrating pdf within certain limits) is not that much significant and pdf can be used instead of probability measure.
Is my opinion correct?
Suppose I have a continuous distribution of human heights, then if I want a measure for a chance of height = 7.889. Then obviously probability measure will be of no use. So, can I use the pdf only in this case as a measure.
In this aspect what is the importance of probability measure since we are not much interested in ranges?