Multiple choice

A card is drawn at random from a pack of $52$ cards. The chance that it is either an ace or a heart is ..........

  1. $\cfrac{17}{52}$
  2. $\cfrac{4}{13}$
  3. $\cfrac{1}{4}$
  4. $\cfrac{1}{13}$
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B Correct answer
Explanation

P(Ace or Heart) = P(Ace) + P(Heart) - P(Ace of Hearts) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13.

AI explanation

Using the addition theorem of probability, the required probability is the sum of the probability of drawing an ace and the probability of drawing a heart, minus the probability of drawing the ace of hearts. This gives (4/52) + (13/52) - (1/52) = 16/52. Simplifying this fraction yields 4/13.

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