In a particular state a major flood happens once every 5 yea

In a particular state, a major flood happens once every 5 years on average. If you can assume floods are independent, and that two floods cannot happen simultaneously, find the following:

(a) The probability that a flood happens within the first 10 years.

(b) The probability that a flood happens 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.

Solution

(c) The expected time until a flood happens, and the standard deviation.