The lifetimes of lightbulbs made in a large factory are exponentially distributed with a mean lifetime of 200 days. The lifetimes of lightbulbs made in a small factory are exponentially distributed with a mean lifetime of 300 days. Five out of every eight lightbulbs are made in the large factory and three out of every eight lightbulbs are made in the small factory. (a) Write down the probability that a lightbulb i) made in the large factory lasts longer than 250 days; ii) made in the small factory lasts longer than 250 days. (b) Calculate the probability that a lightbulb chosen at random lasts longer than 250 days. (c) A given lightbulb has lasted longer than 250 days, calculate the probability that it was made in the large factory.