2. [25 points] A manufacturing process produces a mix of "good" and "bad" memory chips. The lifetime of good chips is modeled as an exponential random variable, with parameter a, whereas the lifetime of bad chips is an exponential random variable with parameter 1000a. Suppose that the fraction of good chips is (1-p) and the fraction of bad chips is p. We select a chip at random. What is the probability that the randomly selected chip is still functioning after t seconds