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 April 7th, 2010, 09:41 PM #1 Senior Member   Joined: Dec 2009 Posts: 150 Thanks: 0 simple probability Suppose X is a discrete random variable on the set of positive integers such that for each positive integer n, the probability that X = n is . If Y is another random variable with the same probability distribution and X and Y are independent, what is the probability that the value of at least on of the variables X and Y is greater than 3? Is the following correct? P(X 3) = = So P(X > 3) = 1 - 7/8 = 1/8 So P(X > 3 AND Y 3) = P(X>3)*P(Y 3) = (1/ *(7/ = 7/64. I believe you can separate the probability like I just did because of the independence, no? Then P(Y > 3 AND X 3) = 7/64 too because it's the same thing really when they're independent. The last case is both of them greater than 3, which is P(X > 3 AND Y > 3) = P(X > 3)*P(Y > 3) = (1/ (1/ = 1/64 Since any one of these possibilities satisfies the requirement, we simply add their probabilities (OR -> + , AND -> *) to get 7/64 + 7/64 + 1/64 = 15/64 please tell me if I made any mistakes, I know this is the right answer, but I want my thought process to be right too. April 8th, 2010, 09:23 AM #2 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: simple probability That's fine. Somewhat simpler: 7/8 chance of being at most 3, so 49/64 chance of both being at most 3, so 1 - 49/64 = 15/64 of at least one being greater than 3. April 8th, 2010, 11:36 AM #3 Senior Member   Joined: Dec 2009 Posts: 150 Thanks: 0 Re: simple probability Tremendously helpful. This was a GRE math subject test question, and of course speed is very important. Thanks for confirming my tedious reasoning to boot. Tags probability, simple Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post lun123 Advanced Statistics 1 October 6th, 2013 05:21 PM ChidoriPOWAA Probability and Statistics 2 August 26th, 2013 03:02 PM maxgeo Probability and Statistics 1 April 23rd, 2013 09:37 AM Tyster Algebra 2 September 27th, 2009 04:48 PM mikeportnoy Advanced Statistics 2 September 27th, 2008 09:10 PM

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