The probability that a radioactive substance will decay at time is modeled by the density function , for , and for . The positive constant depends on the material, and is called the decay rate. Consider two materials with decay rates and , which decay independently of each other. Write the joint density function for the probability that the first material decays at time and the second at time , then find the probability that the first substance decays before the second if and . Enter the exact answer. The probability is Enter your answer in accordance to the question statement .