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In a city there is 85% chance that a rainy day started cloudy. However, only 65%...

In a city there is 85% chance that a rainy day started cloudy. However, only 65% of all days in the city start cloudy. Using Bayes' theorem, calculate at least how many days, on average, it must rain in order to know that the data given are wrong? I have he probabilities P(cloud) = 0.65 and P(cloud | rain) = 0.85.

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Answer #1

P(Cloud)=0.65

P(Cloud/Rain)=.85

We use bays theorem , formula is given below

P(Rain|Cloud) = P(Rain) *P(Cloud|Rain)/P(Cloud)

Here we want to find averaage no. Of days of rain

But we don't have the Probability of P(Rain/Cloud) which is necessary to find P(Rain)

I think data is incomplete

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