1. The problem statement, all variables and given/known data Of the three independent events E1 , E2 and E3, the probability that only E1 occurs is α, only E2 occurs is β and only E3 occurs is γ. Let the probability p that none of the events E1 , E2 and E3 occurs satisfy the equations ## (α - 2β) p = αβ ## and ## (β - 3γ) p = 2βγ ##. All the given probabilities are assumed to lie in the interval (0,1). Then, (Probability of occurrence of E1) / (Probability of occurrence of E3) = Answer is 6. 2. Relevant equations 3. The attempt at a solution http://s3.amazonaws.com/minglebox-p...ata-0000-fdbffe7622c53ecd0122c5c50d0b0334.gif I don't know how to use those equations. All I know is what regions α, β, γ and p represent. α ≡ region 1, β ≡ region 3, γ ≡ region 7 and 1 - regions(1+2+3+4+5+6+7) = p. How do I proceed?