A particular species of fish makes an annual migration up a river. On a particular day there is a probability of 0.4 that the migration will start. If it does then an observer will have to wait $T$ minutes before seeing a fish, where $T$ has an exponential distribution with mean 20 (i.e. an exponential(0.05) distribution). If the migration has not started then no fish will be seen.  

(a) Find the conditional probability that the migration has not started given that no fish has been seen after one hour.   
(b) How long does the observer have to wait without seeing a fish to be 90% sure that the migration has not started?  