Multiple choice

A pack of cards contains $4$ aces , $4$ kings , $4$ queens and $4$ jacks . Two cards are drawn at random . The probability that at least one of these in an ace, is

  1. $\dfrac{9}{{20}}$
  2. $\dfrac{3}{{16}}$
  3. $\dfrac{1}{6}$
  4. $\dfrac{1}{9}{\text{ }}$
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A Correct answer
Explanation

Total cards = 16. Probability of no ace = (12/16) * (11/15) = (3/4) * (11/15) = 11/20. Probability of at least one ace = 1 - 11/20 = 9/20.

AI explanation

The total number of ways to draw two cards from the 16 cards is 16C2, which equals 120. The number of ways to draw two cards such that neither is an ace is 12C2, which equals 66. The probability of at least one ace is 1 minus (66/120), which equals 54/120, and simplifying this fraction gives 9/20.

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