Evenats A and B are mutually exclusive. Which of the

Daniell Phillips 2021-12-19 Answered
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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Expert Answer

Jim Hunt
Answered 2021-12-20 Author has 2151 answers
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
Answered 2021-12-21 Author has 3769 answers
b. P(A U B) = P(A) + P(B).
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RizerMix
Answered 2021-12-29 Author has 9821 answers

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.

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Relevant Questions

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