A city depends on the flow of a nearby river for its water supply. If the discha

Question

A city depends on the flow of a nearby river for its water supply. If the discharge drops below a base level of 30 m3/s, various emergency actions begin. After two consecutive days of sub-base flow, a small reservoir is brought online; after 10 consecutive days of sub-base flow, water must be piped in from a nearby town. River discharge records have been assessed to determine the exceedence probability of the two-day drought (70%) and the 10-day drought (20%). Determine the following: the probability of having to utilize the reservoir at least once in the next two years; the probability of not having to rely on the reservoir in the next two years; the probability of having to rely on the reservoir during each of the next two years; and the probability of having to rely on the reservoir exactly once in the next two years.

Explanation / Answer

A) X is binomial with p=.7, q=.3, n=2 ans=P (X >= 1)=1-P(X=0)=1-(.3)^2=1-.09=.91 b)using above P(x=0)=.09 ... see above c) y binomial, p=.7,q=.3,n=1 P(y >=1)=1-.3=.7 answer =>7(.7)=.49 d) Using x from a P(x=1)=2(.7).3=.42

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