- #1

gajohnson

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- 0

## Homework Statement

This problem introduces a simple meteorological model, more complicated

versions of which have been proposed in the meteorological literature. Consider

a sequence of days and let Ri denote the event that it rains on day i. Suppose

that P(R | R ) = α and P(Rc | Rc ) = β. Suppose further that only today’s i i−1 i i−1

weather is relevant to predicting tomorrow’s; that is, P ( Ri | Ri −1 ∩ Ri −2 ∩ · · · ∩ R0) = P(Ri | Ri−1).

a. If the probability of rain today is p, what is the probability of rain tomorrow?

b. What is the probability of rain the day after tomorrow?

c. What is the probability of rain n days from now? What happens as n approaches infinity?

## Homework Equations

NA

## The Attempt at a Solution

Parts a and b are easy enough--just simple applications of the Law of Total Probability. However, I am having trouble with part c. Any help would be greatly appreciated.

It does appear that this question was previously asked, and someone gave this idea: p(⋂i=1nRi), but I'm not sure how to see this.

Thank you!

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