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 $$(\alpha - 2\beta) p = \alpha \beta$$ and $$(\beta - 3\gamma) p = 2 \beta \gamma$$. All the given probabilities are assumed tolie in the interval (0, 1).
Then $$\frac{Probability of occurrence of E_1}{Probability of occurrence of E_3} = $$