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# Probability of rain?

#### Kyx

I was reading a book about innumeracy and one of the chapters was on probability. This weather woman said 'there is a 50% chance of rain on Saturday, and a 50% chance of rain on Sunday, so the chance of rain this weekend is 100%'

Obviously she was wrong, but it got me thinking how would one calculate the probability of rain that weekend?

I decided to make it simpler by saying P(rain on Saturday) = 0.5 and P(rain on Sunday) = 1.0

This obviously means that P(rain this weekend) = 1.0

I then used trial and error to calculate the chance of rain that weekend

I started with P(rain on Saturday) x P(rain on Sunday) but that gives 0.5

Then I tried P(no rain this weekend) = P(no rain on Saturday) x P(no rain on Sunday) and this gives 0.0

Therefore P(rain this weekend) = 1 - P(no rain this weekend) = 1.0

Using this method, P(rain this weekend) = 0.75 or 75% for the original statement.

Is this the best way to calculate the chance of rain?

#### vedur

Actually I believe that the correct answer would be 50%.

At first I thought that even if you split the time up into hours, then the chance of rain would still be 50% for every hour.

But now I would go as far as saying that the chance of raining on the weekend is dependent of the maximum probability. E.g if it's 20% for Saturday and 80% for Sunday then for the weekend it is 80%. I might be wrong.

By the way, how did you calculate P(rain on Saturday) x P(rain on Sunday) to give 0.5?

#### Kyx

vedur wrote:Actually I believe that the correct answer would be 50%.

At first I thought that even if you split the time up into hours, then the chance of rain would still be 50% for every hour.

But now I would go as far as saying that the chance of raining on the weekend is dependent of the maximum probability. E.g if it's 20% for Saturday and 80% for Sunday then for the weekend it is 80%. I might be wrong.

By the way, how did you calculate P(rain on Saturday) x P(rain on Sunday) to give 0.5?

This was using P(rain on Saturday) = 0.5 and P(rain on Sunday) = 1.0

Clearly 0.5 x 1.0 = 0.5 :p

And regarding P(rain on Saturday) = 0.5 and P(rain on Sunday) = 0.5:

P(rain on Saturday OR rain on Sunday) = 1 - P(No rain Saturday AND No rain Sunday)

P(No rain Saturday) = 0.5 and P(No rain Sunday) = 0.5

Hence, P(No rain Saturday AND No rain Sunday) = P(No rain Saturday) x P(No rain Sunday) = 0.5 x 0.5 = 0.25

P(rain on Saturday OR rain on Sunday) = 1 - P(No rain on Saturday AND No rain Sunday) = 1 - 0.25 = 0.75 