Multiple choice

A card is drawn at random from a well-shuffled deck of $52$ cards. Find the probability that it will be a spade or a king.

  1. $\dfrac{4}{13}$ 
  2. $\dfrac{3}{13}$ 
  3. $\dfrac{2}{13}$ 

  4. none
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A Correct answer
Explanation

There are 13 spades and 4 kings in a deck. One card, the king of spades, is counted in both groups, so the total number of unique favorable cards is 13 + 4 - 1 = 16. The probability is 16/52, which simplifies to 4/13.

AI explanation

Using the addition theorem of probability, the probability is P(Spade) + P(King) - P(King of Spades). Substituting the values gives 13/52 + 4/52 - 1/52, which equals 16/52. Simplifying this fraction gives 4/13.

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