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If P(A) = 2/3 and P(B) = 1/4, what is P((A or B) or (A and B))?

I believe it to be:

P(A or B) = 11/12

P(A and B) = 2/12

Therefore 11/12 + 2/12 = 13/12. Am I correct?

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1 Answer

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Your answer cannot be correct, since it is larger than $1$.

It is not specified whether $A$ and $B$ are independent, and this would affect the result, but in most problems like this it's true so I'll assume it is for this answer.

$P((A\cup B)\cup(A\cap B))$ can be reduced by set theory to just $P(A\cup B)$. $P(A\cap B)=\frac2{12}$ is correct. $P(A\cup B)$ must then be calculated by inclusion-exclusion as $\frac23+\frac14-\frac2{12}=\frac9{12}=\frac34$.

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