Let there be three independent events E_1, E_2 and E_3. The probability that only E_1 occurs is α, only E_2 occurs is β and only E_3 occurs is γ. Let…

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