Multiple choice

A card is drawn from a deck of cards. What is the probability that it is either a spade or an ace or both

  1. $\dfrac{7}{13}$
  2. $\dfrac{10}{13}$
  3. $\dfrac{4}{13}$
  4. $\dfrac{5}{13}$
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C Correct answer
Explanation

P(Spade or Ace) = P(Spade) + P(Ace) - P(Spade and Ace). P(Spade) = 13/52, P(Ace) = 4/52, P(Spade and Ace) = 1/52. (13+4-1)/52 = 16/52 = 4/13.

AI explanation

The pack has 52 cards, so the total number of outcomes is 52. There are 13 spades and 3 additional aces (since one ace is already counted among the spades), giving 16 favorable outcomes. By the classical definition of probability, the probability is the ratio of favorable outcomes to total outcomes, which is 16/52 or 4/13.

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