Let there be three independent events E_{1},E_{2} and E_{3}. The probabolity that only E_{1} occurs is \alpha, only E_{2} occurs is \beta and only  E_{3} occurs  is \gamma. Let 'p' denote the probability of none of events occurs that satisfies the equation \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 ( 0,1 \right ). Then, \frac{\text{Probability of occurrence of E}_{1}}{\text {Probability of occurrence of E}_{3}} is equal to _______________.
Option: 1 5
Option: 2 6
Option: 3 7
Option: 4 8

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