Mutually exclusive event means Event A and Event B do not have any common region.

That means

\(\displaystyle{P}{\left({A}\cap{B}\right)}={0}\)

We know addition rule of probability

\(\displaystyle{P}{\left({A}\cup{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}-{P}{\left({A}\cap{B}\right)}\)

We have given Event A and B are mutually exclusive \(\displaystyle{P}{\left({A}\cap{B}\right)}={0}\)

\(\displaystyle{P}{\left({A}\cup{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}-{0}\)

so we get.

\(\displaystyle{P}{\left({A}\cup{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}\)

Correct choice is ( B )