<p>Two cards are drawn one by one randomly from a pack of 52 cards. Then find the probability that both of them are king.</p>
Step-by-Step Solution
Key Concept: When drawing without replacement, the probability of the second event depends on the outcome of the first. Use conditional probability: P(both kings) = P(1st king) × P(2nd king | 1st king).
<p><strong>Step 1:</strong> Identify the setup. A standard pack has 52 cards with 4 kings. Cards are drawn one by one without replacement.</p><p><strong>Step 2:</strong> Find P(1st card is king) = 4/52 = 1/13</p><p><strong>Step 3:</strong> Find P(2nd card is king | 1st card was king). After removing one king, 3 kings remain out of 51 cards. So P(2nd king | 1st king) = 3/51 = 1/17</p><p><strong>Step 4:</strong> Apply multiplication rule for dependent events: P(both kings) = (4/52) × (3/51) = (1/13) × (1/17) = 1/221</p><p><strong>Alternative approach:</strong> P(both kings) = C(4,2)/C(52,2) = 6/1326 = 1/221</p><p>∴ Answer: <strong>1/221</strong></p>
Correct Answer: 1/221