Suppose a product must pass through two machines in order to complete its production process. Let X and X2 be the time each machine takes to complete its task. Moreover, X, and X; are exponentially distributed random variables with mean rate 0.2 and 0.333 respectively. If the total time to produce the product is 1 hours, what is the probability that machine I will take between 10 and 30 minutes to complete the job? (Hint: first find conditional density of X, given that X1+X2=1).