Probability AITS for IITJEE

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 equation $(\alpha - 2\beta) p = \alpha \beta$ and $(\beta - 3\gamma) p = 2\beta \gamma$ . All th given probabilities are assumed to lie in the interval $(0,1)$ .

Evaluate $\dfrac{\text{Probability of occurence of }E_1}{\text{Probability of occurence of }E_3}$ .