Of the three independent events $E _ { 1 } , E _ { 2 }$ and $E _ { 3 }$, the probability that only $E _ { 1 }$ occurs is $\alpha$, only $E _ { 2 }$ occurs is $\beta$ and only $E _ { 3 }$ occurs is $\gamma$. Let the probability $p$ that none of events $E _ { 1 } , E _ { 2 }$ or $E _ { 3 }$ occurs satisfy 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 $( 0,1 )$. $$\text { Then } \frac { \text { Probability of occurrence of } E _ { 1 } } { \text { Probability of occurrence of } E _ { 3 } } =$$
Of the three independent events $E _ { 1 } , E _ { 2 }$ and $E _ { 3 }$, the probability that only $E _ { 1 }$ occurs is $\alpha$, only $E _ { 2 }$ occurs is $\beta$ and only $E _ { 3 }$ occurs is $\gamma$. Let the probability $p$ that none of events $E _ { 1 } , E _ { 2 }$ or $E _ { 3 }$ occurs satisfy 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 $( 0,1 )$.
$$\text { Then } \frac { \text { Probability of occurrence of } E _ { 1 } } { \text { Probability of occurrence of } E _ { 3 } } =$$