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April 5th, 2013, 10:59 PM  #1 
Senior Member Joined: Jul 2012 Posts: 225 Thanks: 0  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 DA  it's raining in city A. same for events DB and DC. event CD  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 
April 6th, 2013, 11:27 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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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