, 2016

Line segment $PQ$ is vertical if $Q$ is chosen from the points in the column in which $P$ lies. This column contains 9 points other than $P$ which could be chosen to be $Q$ so that $PQ$ is vertical. Line segment $PQ$ is horizontal if $Q$ is chosen from the points in the row in which $P$ lies. This row contains 9 points other than $P$ which could be chosen to be $Q$ so that $PQ$ is horizontal. Each of these 9 points is different from the 9 points in the column containing $P$. Thus, there are $9+9=18$ points which may be chosen to be $Q$ so that $PQ$ is vertical or horizontal. Since there are a total of 99 points to choose $Q$ from, the probability that $Q$ is chosen so that $PQ$ is vertical or horizontal is $\frac{18}{99}$ or $\frac{2}{11}$.