Problem 4: The term one-hundred-year ood is often used to describe a very

severe ood. This term actually has a more precise meaning. By denition,

the probability that a river will meet or exceed its one-hundred-

year ood level in any given year is 1

100. (Similarly, a 20-year-ood

has a probability of 1

20 of occurring in any given year and a 500-year-ood

has a probability of 1

500 of occurring in any given year.) The 100 in a

one-hundred-year ood is an expected value. A ood of that magnitude is

expected to occur on average once every 100 years.

(a) A certain river has not reached its one-hundred-year ood level in the

past 99 years. What is the probability that it will reach its one-hundred-

year ood level next year?

(b) Suppose you decide to buy a house in a one-hundred-year ood plain,

so the probability of your house being ooded in any given year is

1

100 = 1%. Suppose you own this house for 20 years. Take the following

steps to compute the probability that your house will be ooded at

least once during this 20-year period.

(i) In any given year, what is the probability that your house will NOT

be ooded?

(ii) What is the probability that your house will NOT be ooded over

the entire 20-year period? (Hint: Remember that we multiply when

counting independent events happening in succession.)

(iii) Use the Law of Complements to determine the probability that

your house will be ooded at least once over the 20-year period.