Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is $\alpha$, only E2 occurs is $\beta$ and only E3 occurs is $\gamma$. Let 'p' denote the probability of none of events occurs that satisfies the equations ($\alpha$ $-$ 2$\beta$)p = $\alpha$$\beta$ and ($\beta$ $-$ 3$\gamma$)p = 2$\beta$$\gamma$. All the given probabilities are assumed to lie in the interval (0, 1).Then, $\frac{Probability\ of\ occurrence\ of\ E_{1}}{Probability\ of\ occurrence\ of\ E_{3}} $ is equal to _____________.

Question

Let there be three independent events E₁, E₂ and E₃. The probability that only E₁ occurs is $\alpha$, only E₂ occurs is $\beta$ and only E₃ occurs is $\gamma$. Let 'p' denote the probability of none of events occurs that satisfies the equations
($\alpha$ $-$ 2$\beta$)p = $\alpha$$\beta$ and ($\beta$ $-$ 3$\gamma$)p = 2$\beta$$\gamma$. All the given probabilities are assumed to lie in the interval (0, 1).

Then, $\frac{Probability\ of\ occurrence\ of\ E_{1}}{Probability\ of\ occurrence\ of\ E_{3}} $ is equal to _____________.

Correct Answer

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