One card is drawn at random from a well-shuffled pack of 52 playing cards. What is the probability that the card is a face card (a jack, queen or king) or a club, or both?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{11}{26}\)
When two groups overlap, the cards in both groups must be counted only once: n(A or B) = n(A) + n(B) − n(both).
Face cards: 3 in each of 4 suits \(=12\)
Clubs \(=13\)
Cards that are both: the jack, queen and king of clubs \(=3\)
Face card or club \(=12+13-3=22\)
Probability \(\displaystyle =\frac{22}{52}=\frac{11}{26}\)