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07-02-2018
Mathematics

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P(A) = 1/2, P(B) = 1/3, P(A or B) = 2/3. Are A and B mutually exclusive?

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LammettHash LammettHash

07-02-2018

[tex]A[/tex] and [tex]B[/tex] are mutually exclusive if

[tex]\mathbb P(A)+\mathbb P(B)=\mathbb P(A\cup B)[/tex]

You have

[tex]\dfrac12+\dfrac13=\dfrac56\neq\dfrac23[/tex]

so the answer is no.

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