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 November 17th, 2012, 07:11 PM #1 Newbie   Joined: Nov 2012 Posts: 1 Thanks: 0 probability set theory - probability of x out of n events am having an issue related to probability set theory with intersection/union terms. When calculating the union of terms or in other words, the probability that at least one term "fails", it can be written as the following for three terms: P(A+B+C) = P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC). My question is how to assess a problem similar to this when we are looking at the probability at least x terms out of n terms fail. For example, at least 2 out of 4. Or at least 7 out of 10. I thought I came up with the correct answer when looking at a system of only 4 terms. For example: P(at least 2 out of 4) = P(AB)+P(AC)+P(AD)+P(BC)+P(BD)+P(CD) -2*(P(ABC)+P(ABD)+P(ACD)+P(BCD)) +3*(P(ABCD)) P(at least 3 out of 4) = P(ABC)+P(ABD)+P(ACD)+P(BCD) -3*(P(ABCD)) This works here. In fact, it works for P(at least 2 out of n) and P(at least (n-1) out of n) for all cases of n. However it does not work for the situations in between. I am looking for an analog formula that can evaluate any case for the probability of at least x out of n failure. Any help with be appreciate. Thanks! Tags events, probability, set, theory 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 jman115 Advanced Statistics 3 January 19th, 2012 03:30 AM hoyy1kolko Probability and Statistics 1 April 12th, 2011 08:10 PM hoyy1kolko Probability and Statistics 1 April 11th, 2011 12:23 PM daivinhtran Advanced Statistics 1 April 9th, 2011 02:03 PM SidT Algebra 3 September 24th, 2009 03:47 AM

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