Multiple choice

A card is drawn randomly from a pack of $52$ cards. Find the probability that the card drawn is neither a heart nor a king

  1. $\dfrac {9}{13}$
  2. $\dfrac {9}{11}$
  3. $\dfrac {7}{12}$
  4. $\dfrac {7}{13}$
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A Correct answer
Explanation

Total cards = 52. Hearts = 13. Kings = 4. Heart-Kings = 1. Union of Hearts and Kings = 13 + 4 - 1 = 16. Neither heart nor king = 52 - 16 = 36. Probability = 36 / 52 = 9 / 13.

AI explanation

The probability of a card being either a heart or a king is found by adding the probability of a heart, which is 13 over 52, to the probability of a king, which is 4 over 52, and subtracting the probability of the king of hearts, which is 1 over 52. This gives 16 over 52, which is the probability of the union of the two events. The probability that a card is neither a heart nor a king is 1 minus 16 over 52, which is 36 over 52. This fraction simplifies to 9 over 13.

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