A fair $6$-sided die is rolled. What is the probability of rolling an **even number** OR a **multiple of $3$**?
A$\dfrac{1}{2}$
B$\dfrac{2}{3}$
C$\dfrac{5}{6}$
D$1$
Answer & Solution
Correct answer: B. $\dfrac{2}{3}$
Even: $\{2, 4, 6\}$ → $P = 3/6$. Multiple of 3: $\{3, 6\}$ → $P = 2/6$. Overlap (even AND multiple of 3): $\{6\}$ → $P = 1/6$.
Inclusion-exclusion: $P(\text{even or mult-3}) = \tfrac{3}{6} + \tfrac{2}{6} - \tfrac{1}{6} = \tfrac{4}{6} = \tfrac{2}{3}$.
Direct count: favourable outcomes $\{2, 3, 4, 6\}$ — that's $4$ of $6$ ✓.
- Trap C ($5/6$) forgets the overlap subtraction.
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