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April 5th, 2013, 10:59 PM   #1
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Check my answer please - conditional probability (bayes)

hey all, could you give comments and check my answer? It doesn't show in the textbook.

OriaG is randomly choosing a city to visit. city A, city B, and city C.
The chance it will rain on city A is

The chance it will rain on city B is

The chance it will rain on city C is

When OriaG arrived at his city of choice, it was raining.
What is the chance OriaG chose to visit city C?

My solution:
event A - OriaG chose to visit city A. same for events B and C.
event D - It's raining somewhere
event D|A - it's raining in city A. same for events D|B and D|C.
event C|D - OriaG chose city C and it's raining.



we we're given

and we are asked to calculate , use Bayes formula:



Final answer: The chance OriaG chose a rainy city and it was C is
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April 6th, 2013, 11:27 AM   #2
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Re: Check my answer please - conditional probability (bayes)

Yes, that is what I get doing the problem a different way: Imagine a set of 36 "(city, weather)" pairs. 12 each refer to A, B, and C. Of the "A" pairs, 1/3, or 4, are (A, rain). Of the "B" pairs, 1/4, or 3, are (B,rain). Of the "C" pairs, 1/6, or 2, are (C, rain). That' makes a total of 9 "(city, weather)" pairs that have "rain". Of those, 2 are "City C" so the probability he/she went to city C given that it was raining is .
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