In the specific state, a major flood takes place once every 5 years on average. If you can assume floods are independent, and that two floods can't take place simultaneously, determine the following:
(a) The probability that the flood takes place in the first 10 years.
(b) The probability that the flood takes place after the first 6 years.
(c) The expected time until a flood happens, and the standard deviation.
(d) Find the 50th percentile of the time until a flood.