How to calculate the return period of a flood?

 Question:  A residential area located near the Neebing River in Thunder Bay used to be flooded in 5 of the 20 years before the Thunder Bay Floodway became operational in 1983. What is the return period of this flood? What is the probability that the residential area will not be flooded next year? What is the probability that the residential area will be flooded at least once in the next 3 years?

Answer: 

Return period of the flood is 4 years. Since it occurs 5 years in every 20 years.

Return period is denoted by 'T'

T = 4

Now , probability of the flood ,p = 1/T = 1/5 = 0.25

Now, probability that the residential area will not be flooded in the next year = q

q = 1- p = 1-0.25 = 0.75

Again, the probability that the residential area will be flooded at least once in next 3 years =

1 - q^3 = 1 - 0.75 ^3 = 0.578

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