# Evenats A and B are mutually exclusive. Which of the

Evenats A and B are mutually exclusive. Which of the following statements is also true?
a. $$\displaystyle{P}{\left({A}\cap{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}$$
b. $$\displaystyle{P}{\left({A}\cup{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}$$
c. A and B are also independent
d. $$\displaystyle{P}{\left({A}\cup{B}\right)}={P}{\left({A}\right)}{P}{\left({B}\right)}$$

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Jim Hunt
We have given A and B are mutually exclusive event.
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 )
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Dawn Neal
b. P(A U B) = P(A) + P(B).
RizerMix

We know $$P(A\cup B) =P(A)+P(B)-P(A∩B),$$
Since A and B,Mutually Exclusive $$P(A∩B) =0,$$
So $$P(A \cup B)=P(A)+P(B)$$
Option d is correct option.