# Predicting component failture with joint density functions

A device contains two components. The device fails if either component fails. The joint density function of the lifetimes of the components, measured in hours, is f(s, t) , where $0 < s < \infty$ and $0 < t < \infty$. What is the probability that the device fails during the first half hour of operation, expressed in terms of the cumulative distribution function F (s, t)? Thanks for your help (Bow)
A device contains two components. The device fails if either component fails. The joint density function of the lifetimes of the components, measured in hours, is f(s, t) , where $0 < s < \infty$ and $0 < t < \infty$. What is the probability that the device fails during the first half hour of operation, expressed in terms of the cumulative distribution function F (s, t)? Thanks for your help (Bow)