Let x and x, denote the lifetimes (in months) of bulbs produced at factories and f respectively. the random variables x, and x are exp(1/8) and exp(1 /2) respec

Let X and X, denote the lifetimes (in months) of bulbs produced at factories and F respectively. The random variables X, and X are Exp(1/8) and Exp(1 /2) respectively. A shop procures 80% ofits supply of bulbs from factory R and 20% from factory E.A randomly selected bulb from the shop is put on test and is found to be working after 4 months. What is the probability that it was procured trom factory P ?