In a particular state, a major flood happens once every 5 years on average. You may assume an exponential distribution. 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. begin{tabular} hline Final Numerical Answer Below hline end{tabular} (b) The probability that a flood happens after the first 6 years. begin{tabular}c hline Final Numerical Answer Below hline end{tabular} (c) The expected time until a flood happens, and the standard deviation. (d) Find the 50 th percentile of the time until a flood.