Multiple choice

Two cards are drawn one by one at random from a pack of $52$ cards. The proabability that both of them are king is

  1. $\cfrac { 2 }{ 13 } $
  2. $\cfrac { 1 }{ 169 } $
  3. $\cfrac { 1 }{ 221 } $
  4. $\cfrac { 30 }{ 221 } $
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C Correct answer
Explanation

The probability of drawing two kings without replacement is (4/52) × (3/51). This simplifies to 1/221, because there are 4 kings among 52 cards and then 3 kings among the remaining 51 cards.

AI explanation

Since the cards are drawn one by one without replacement, the multiplication theorem of probability applies. The probability of getting a king on the first draw is 4/52, and the probability of getting a second king from the remaining 51 cards is 3/51. Multiplying these gives 4/52 times 3/51, which simplifies to 1/221.

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