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Categorise the weather as either "wet" or "dry". The
probability that tomorrow is "wet" depends upon the weather for
some previous time.
We use the notation :
p(tomorrow is wet  today is wet)
for the conditional probability that tomorrow is wet given
that today is wet.

Suppose that  p(tomorrow is wet  today is wet) = 0.7 
and  p(tomorrow is wet  today is dry) = 0.2 
(i) write down p(tomorrow is dry  today is wet)
and p(tomorrow is dry  today is dry)
On 1^{st} June, when you are planning a picnic, the weather will be either wet or dry. Let p(June 1st is wet) = p and consequently p(June 1st is dry) = 1  p
(ii) Write down p(June 2nd is wet) in terms of p.
Let p _{n} denote the probability that the weather on day n is wet given that the weather the day before is wet. Now simplify the problem by making the assumption that the weather on any given day depends only on the weather the day before and not on the weather before then.
Use an iterative technique (with your calculator if you wish) to find
(iii) p(July 1 ^{st} is wet  June 1 ^{st} is wet)
(iv) p(July 1 ^{st} is wet  June 1 ^{st} is dry)
(v) What do the answers to (iii) and (iv) tell you about longterm future weather?