SOLUTION: In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 an

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Question 62832: In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of rain on a day following a nonrainy day is 0.250. Find the probability that January 1st and January 2nd are rainy and that January 3rd and 4th are not rainy given that December 31st was clear all day.
Answer by stanbon(75887) About Me  (Show Source):
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In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of rain on a day following a nonrainy day is 0.250. Find the probability that January 1st and January 2nd are rainy and that January 3rd and 4th are not rainy given that December 31st was clear all day.
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P(rain on Jan1st)=0.25
P(rain on Jan2nd)=0.6
P(no rain on Jan2rd)=0.4
P(no rain on Jan3rd)=0.75
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Prob of all of this is the product of all of these = 0.045
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Cheers,
Stan H.