Let B_i(i=1,2,3) be three independent events in a sample space. The probability that only B_1 occur is α, only B_2 occurs is β and only B_3 occurs is…

Let $\displaystyle \mathrm{B}_i(i=1,2,3)$ be three independent events in a sample space. The probability that only $\displaystyle B_1$ occur is $\displaystyle \alpha$, only $\displaystyle B_2$ occurs is $\displaystyle \beta$ and only $\displaystyle B_3$ occurs is $\displaystyle \gamma$. Let $\displaystyle p$ be the probability that none of the events $\displaystyle \mathrm{B}_i$ occurs and these $\displaystyle 4$ probabilities satisfy the equations $\displaystyle (\alpha-2 \beta) \mathrm{p}=\alpha \beta$ and $\displaystyle (\beta-3 \gamma) \mathrm{p}=2 \beta \gamma$ (All the probabilities are assumed to lie in the interval $\displaystyle (0,1)$). Then $\displaystyle \frac{\mathrm{P}\left(\mathrm{B}_1\right)}{\mathrm{P}\left(\mathrm{B}_3\right)}$ is equal to \_\_\_\_.