In the following Venn diagram circles A and B represent two events:

The probability of the union of shaded region will be

From the given Venn diagram the shadow region is 

$n\left(A\right)+n\left(B\right)-n(A\cap B)$.

Probability of the union of the shaded region is 

$\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)-\mathrm{P}(\mathrm{A}\cap \mathrm{B})$