Multiple choice

From a pack of 52 cards. two are drawn at random. Find the chance that one is a knave and the other a queen.

  1. $\dfrac{8}{663}$
  2. $\dfrac{1}{6}$
  3. $\dfrac{1}{9}$
  4. $\dfrac{1}{12}$
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A Correct answer
Explanation

There are 4 knaves and 4 queens in a deck. The number of ways to choose one knave and one queen is 4 * 4 = 16. The total number of ways to draw two cards is 52C2 = (52 * 51) / 2 = 1326. The probability is 16 / 1326 = 8 / 663.

AI explanation

The total number of ways to draw two cards from a 52-card deck is 52C2, which equals 1326. A standard deck contains 4 knaves and 4 queens, so the number of favorable ways is 4 multiplied by 4, which is 16. The probability is 16/1326, which simplifies by dividing the numerator and denominator by 2 to 8/663.

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