A study of daily rainfall in Ashland Kentucky has shown that

A study of daily rainfall in Ashland, Kentucky has shown that in July the probability of a rainy day following a rainy day is 0.444, a dry day following a dry day is 0.724, a rainy day following a dry day is 0.276, and a dry day following a rainy day is 0.556. If it is observed that a certain July day is rainy, (Hint: use the definition of conditional probability)

a. What is the probability that the next two days will also be rainy?

b. What is the probability that the next day will be rainy followed by a dry day?

c. What is the probability that the next two days will be dry?

Solution

Let

R = rainy
D = dry

Thus,

a)

P(R, R) = P(R|R) R(R|R) = 0.444*0.444 = 0.197136 [answer]

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b)

P(R, D) = P(R|R) P(D|R) = 0.444*0.276 = 0.122544 [answer]

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c)

P(D, D) = P(D|R) P(D|D) = 0.276*0.724 = 0.199824 [answer]