Let there be three independent events $\mathrm{E}_1, \mathrm{E}_2$ and $E_3$. The probability that only $E_1$ occurs is $\alpha$, only $E_2$ occurs is $\beta$ and only $\mathrm{E}_3$ occurs is $\gamma$. Let ' p ' denote the probability of none of events occurs that satisfies the equations $(\alpha-2 \beta) \mathrm{p}=\alpha \beta$ and $(\beta- 3 \gamma) \mathrm{R}=2 \beta \gamma$. All the given probabilities are assumed to lie in the interval $(0,1)$. Then, $\frac{\text { Probability of occurrence of } E_1}{\text { Probability of occurrence of } E_3}$ is equal to