Mathematics - Probability Question with Solution | TestHub

Of the three independent events${\text{E}}_1$,${\text{E}}_2$and${\text{E}}_3$, the probability that only${\text{E}}_1$occurs is$\alpha$, only${\text{E}}_2$occurs is$\beta$and only${\text{E}}_3$occurs is$\gamma$. Let the probability$p$that none of events${\text{E}}_1$,${\text{E}}_2$or${\text{E}}_3$occurs satisfy the equations$\left(\alpha -2\beta \right)p=\alpha \beta$and$\left(\beta -3\gamma \right)p = 2\beta \gamma$. All the given probabilities are assumed to lie in the interval$\left(\text{0, 1}\right)$.
Then$\frac{{\text{Probability of occurrence of E}}_1}{{\text{Probability of occurrence of E}}_3}=$​