<p>Find the probability of drawing either an ace or a king from a pack of card in a single draw.</p>
Step-by-Step Solution
Key Concept: Use the addition rule for mutually exclusive events: P(A or B) = P(A) + P(B) when events cannot occur simultaneously. Aces and kings are distinct cards, so these events don't overlap.
<p><strong>Step 1:</strong> Identify the favorable outcomes.</p><p>Number of aces in a standard deck = 4</p><p>Number of kings in a standard deck = 4</p><p>Total favorable outcomes = 4 + 4 = 8</p><p><strong>Step 2:</strong> Apply the addition rule for mutually exclusive events.</p><p>Since drawing an ace and drawing a king cannot happen simultaneously:</p><p>P(Ace or King) = P(Ace) + P(King)</p><p>P(Ace or King) = $\dfrac{4}{52} + \dfrac{4}{52} = \dfrac{8}{52}$</p><p><strong>Step 3:</strong> Simplify the fraction.</p><p>$\dfrac{8}{52} = \dfrac{2}{13}$ (dividing numerator and denominator by 4)</p><p>∴ Answer: $\dfrac{2}{13}$</p>
Correct Answer: \(\dfrac{2}{13}\)