The Complement

Something either happens or it does not, so those two chances add up to 1. If the chance of rain tomorrow is $\frac{3}{10}$, the chance of no rain is $1-\frac{3}{10}$, which is $\frac{7}{10}$.

Why subtract from 1? A probability of 1 stands for all the possible outcomes. They split into the ones where the event happens and the ones where it does not, so the second chance is whatever the first leaves over. The event not happening is called the complement.

The complement is quickest when the event itself is awkward to count. The chance of rolling anything except a six is $1-\frac{1}{6}$, which is $\frac{5}{6}$: one subtraction instead of counting five faces.