overlapping distribution

What is the best statistical method to measure the probability of people fitting a certain criteria in my data overlapping with another criteria? I am tasked to display this in a column/bar chart for a simple display of the consequence of its selection on other relevant pots of data.

In engineering, typically we design structures to withstand a certain load. Given that there are uncertainties in both, we apply a factor of safety to give a "buffer" between the computed capacity and the load. Here's my question: If the load has a certain probability distribution and if...