A sample space has three outcomes with $P(\omega_1) = 2P(\omega_2) = 3P(\omega_3)$. What is $P(\omega_1)$?

Explanation

1. 01

   Write $P(\omega_1) = p$; then $P(\omega_2) = \frac{p}{2}$ and $P(\omega_3) = \frac{p}{3}$.

2. 02

   $p + \frac{p}{2} + \frac{p}{3} = \frac{11p}{6} = 1$, so $p = \frac{6}{11}$.