# Let $B_i\left ( i=1,2,3 \right )$ be three independent events in a simple space. The probability that only B1 occur is $\alpha$ , only B2 occur is $\beta$, and only B3 occurs is $\gamma$. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations $\left ( \alpha -2\beta \right )p=\alpha \beta \text{ and } \; \left ( \beta -3\gamma \right )p=2\beta \gamma$(All the probabilities are assumed to lie in the interval (0,1)). Then $\frac{P(B_1)}{P(B_3)}$ is equal to_____ Option: 1 2 Option: 2 3 Option: 3 5 Option: 4 6

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