Of the three independent event `E_(1),E_(2)` and `E_(3)`, the probability that only `E_(1)` occurs is `alpha`, only `E_(2)` occurs is `beta` and only `E_(3)` occurs is `gamma`. If the probavvility p that none of events `E_(1), E_(2)` or `E_(3)` occurs satisfy the equations `(alpha - 2beta)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, `("probability of occurrence of " E_(1))/("probability of occurrence of " E_(3))` is equal to

Explanation

To solve the problem step by step, we will first define the probabilities of the events and then derive the required ratio.

### Step 1: Define the probabilities
Let:
- \( P(E_1) = x \)
- \( P(E_2) = y \)
- \( P(E_3) = z \)

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