We have two light bulbs, A and B. Bulb A has an exponentially distributed lifetime with mean lifetime 4 days i.e lA = 14.Bulb B has an exponentially distributed lifetime with mean lifetime 6 days i.e lB = 1 6 . We select one of the two bulbs at random; each bulb is equally likely to be chosen. Given that the bulb we selected is still working after 12 hours (i.e. 12day), what is the probability that we selected bulb A?Hint: If X stands for the random variable ‘lifetimeâ€TM of the selected bulb, then the statement : “the bulb has an exponentially
distributed lifetime with decay parameter l†implies the following probability P[X x j thebulbselected] = eô€€€lxwhere x represents a particular lifetime. You may need to use Bayesâ€TMs rule to arrive at the required probability.