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May 3rd, 2017, 10:03 AM  #1 
Newbie Joined: Apr 2017 From: Philippines Posts: 2 Thanks: 0  Several Bayesian Probability questions.
1.) If it rains, I do not go sailing. It rains 10% of days; I go sailing 3% of days. If it does not rain, what is the (conditional) probability that I go sailing? Written "p(I go sailing  it does not rain)''? 2.)I am at my office AND not working 2% of the time. I am at my office 10% of the time. What is the conditional probability that I am not working, if I am at my office? 3.) An Urn contains two white marbles and one black marble. A marble is drawn from the Urn without replacement and put aside without my seeing it. Then a second marble is drawn, and it is white. What is the probability that the unknown removed marble is white, and what is the probability that it is black? I would appreciate if you guys can provide a sound solution and a clear explanation. Thanks! 
May 13th, 2017, 07:00 PM  #2 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 561 Thanks: 79 
1. 90% of days it doesn't rain. The probability is 3%/90% = 1/30. 2. I think you're asking: P (not working and at my office)/P (not working) P (not working and at my office) = 2% * 10% = .002 P (not working and not at my office) = 90% = .900 P (not working and at my office)/P (not working) = .002/(.002 + .900) = .002/.902 = 2/902 = 1/451 = .002217294900222 3. I was starting to post multiple steps, but they're not necessary. If the second marble is white, the first marble and the marble not picked are one black and one white in some order, so the probabilities for the first marble are 1/2 each. 

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