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For two events $A$ and $B$, which formula correctly gives the probability of $A\cup B$? 
A$P(A\cup B)=P(A)+P(B)$
B$P(A\cup B)=P(A)P(B)$
C$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
D$P(A\cup B)=\dfrac{P(A)}{P(B)}$
Answer & Solution
Correct answer: C. $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
When adding $P(A)$ and $P(B)$, the overlap $P(A\cap B)$ gets counted twice. So it must be subtracted once, giving $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. The overlapping-region figure illustrates exactly this correction.
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