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[" Of the three independent events "E_(1),F_(2)" and "E_(3)" the probability that only "E_(1)" occurs is a,only is "beta],[" and only "E_(3)" occurs is "gamma" .Let the probability "p" that none of events "E_(1),E_(2)" and "E_(3)" occurs satisfy the "],[" equations "(alpha-2 beta)p=alpha beta" and "(beta-3 gamma)p=3 beta gamma" .All the given probabilities are assumed to lie in "],[" the interval "(0,1)" .Then "(" probability of occurrence of "E_(1))/(" occurrence of "E_(3))=],[" (JEE-Advanced "2013)]

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Of the three independent events E_(1),E_(2),and E_(3), the probability that only E_(1) occurs is alpha only E_(2) occurs is beta, and only E_(3) occurs is gamma. Let the probability p that none of events E_(1),E_(2), or E_(3) occurs satisfy the equations (alpha-2beta)p=alpha betaand (beta-3gamma)p=betagamma. All the given probabilities are assumed to lie in the interval (0,1). Then ("Probability of occurrence of"E_(1))/("Probability of occurence of"E_(3))=______.

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