Probabilities from a histogram
In histograms, the area above any class equals the proportion of values in the class.
The diagram below shows the histogram of a population of 50 values.
Drag with the mouse over some of the histogram classes to highlight them. The proportion of values in the selected classes equals the area above these classes. This is also the probability that a single sampled value is within these classes.
Probabilities from a probability density function
Since the probability density function (pdf) describing an infinite numerical population is a type of histogram, it satisfies the same property.
The probability that a sampled value is within two values, P(a < X < b), equals the area under the pdf.
In the diagram below, again drag with the mouse over the diagram to highlight an interval of values. The probability of getting a value from the interval is equal to the area above that interval.