Solve the below problem:
Q: Let X denote the time between detections of a particle with a Geigercounter and assume that X has an exponential distribution with E(X) = 1.4 minutes. The probabilitythat we detect a particle within 30 seconds of starting the counter isP(X < 0.5 minute) = F (0.5) = 1- e -0.5/1.4 = 0.30In this calculation, all units are converted to minutes. Now, suppose that we turn on the Geiger counter and wait threeminutes without detecting a particle. What is the probability that a particle is detected in the next 30 seconds?