Question 984096: The floodwalls of a city have been designed for a river level that will be exceeded on average once every 50 years.
a) What is the probability that the city will be flooded once in 50 years?
For this, my thinking was the probability would simply be 1 in 50.
b) What is the probability that the city will not be flooded in any of 10 years?
My thought process for this and problem c. would be to use binomial distribution and find the complement of this, to then subtract from 1 to ultimately find the desired probability
c) What is the probability that the city will be flooded at most, 2 out of 10 years?
d) What is the probability of no flood in 50 years?
This I am not sure about. I suppose my thinking is similar to that in part a. If the walls are designed to be exceeded once every 50 years, I'd think the probability of no flood in 50 years would be 0%
Any assistance with problem setup is greatly appreciated.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The expected value is that it will be flooded once in 50 years.
The probability it will be flooded in a given year is 0.02.
You are correct: the probability it will be flooded once is 50C1(0.02(1(0.98)^49=0.372
The probability it won't be flooded in a 10 year period is 0.817, 0.98^10
For c do 0,1,and 2.
Probability of 0 is 0.364, probability of 1 is 0.372,
probability of 2 is 50C2(0.02)^2(0.98)^48=0.171
Therefore, the probability of 0,1,2 is 0.906, the probability it will be flooded at most 2 times.
No flood in 50 years is 0.98^50=0.372 from the above.
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