Varsha lives alone and dislikes cooking, so she goes out for dinner every evening. She has two favourite restaurants, $\text{Dosa Paradise}$ and $\text{Kababs Unlimited}$, to which she travels by local train. The train to $\text{Dosa Paradise}$ runs every $10$ minutes, at $0, 10, 20, 30, 40$ and $50$ minutes past the hour. The train to $\text{Kababs Unlimited}$ runs every $20$ minutes, at $8, 28$ and $48$ minutes past the hour. She reaches the station at a random time between $7:15$ pm and $8:15$ pm and chooses between the two restaurants based on the next available train/ What is the probability that she ends up eating in $\text{Kababs Unlimited}$?
- $\frac{1}{5}$
- $\frac{1}{3}$
- $\frac{2}{5}$
- $\frac{1}{2}$