<p>A coin is tossed and a die is thrown simultaneously. The probability that the outcome is a head or a number greater than 4 on the die is</p>
Step-by-Step Solution
Key Concept: Use addition rule: P(A \cup B) = P(A) + P(B) - P(A \cap B). Here A = head, B = die > 4.
<p>$P(H) = \dfrac{1}{2}$, $P(\text{die} > 4) = \dfrac{2}{6} = \dfrac{1}{3}$.</p><p>Since coin and die are independent: $P(H \cap \text{die}>4) = \dfrac{1}{2} \cdot \dfrac{1}{3} = \dfrac{1}{6}$.</p><p>$P(H \cup \text{die}>4) = \dfrac{1}{2} + \dfrac{1}{3} - \dfrac{1}{6} = \dfrac{3+2-1}{6} = \dfrac{4}{6} = \dfrac{2}{3}$</p>
Correct Answer: C