Multiple choice

One card is drawn from a well-shuffled deck of $52$ cards. Find the probability that the card drawn is a spade or a face card:

  1. $\displaystyle \frac{9}{26}$
  2. $\displaystyle \frac{3}{26}$
  3. $\displaystyle \frac{11}{26}$

  4. None of these
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C Correct answer
Explanation

There are 13 spades and 12 face cards (excluding the 3 spade face cards already counted). Total favorable outcomes = 13 + 9 = 22. Probability = 22/52 = 11/26.

AI explanation

Using the addition theorem of probability, the probability of drawing a spade or a face card is P(Spade) plus P(Face Card) minus P(Spade Face Card). There are 13 spades, 12 face cards, and 3 face cards that are spades among the 52 cards. The calculation is 13/52 plus 12/52 minus 3/52, which equals 22/52, simplifying to 11/26.

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