Of the three independent events \( \mathrm{E}_{1}, \mathrm{E}_{2} \) and \( \mathrm{E}_{3} \), t...

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Of the three independent events \( \mathrm{E}_{1}, \mathrm{E}_{2} \) and \( \mathrm{E}_{3} \), the probability that only \( \mathrm{E}_{1} \) occurs is \( \alpha \), only \( \mathrm{E}_{2} \) occurs is \( \beta \) and only \( \mathrm{E}_{3} \) occurs is \( \gamma \). Let the probability \( \mathrm{p} \) that none of events \( \mathrm{E}_{1}, \mathrm{E}_{2} \) or \( \mathrm{E}_{3} \) occurs satisfy the equati ons \( (\alpha-2 \beta) \mathrm{p}=\alpha \beta \) and \( (\beta-3 \gamma) \mathrm{p}=2 \beta \gamma \). All the given probabilities are assumed of lie in the interval \( (0,1) \).
Then \( \frac{\text { Probability of occurrence of } \mathrm{E}_{1}}{\text { Pr obability of occurrence of } \mathrm{E}_{3}}= \)
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