A card is drawn from a well shuffled pack of 52 cards. Find the probability that it is neither a king nor a heart.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{9}{13}\)
“Neither a king nor a heart” is the opposite of “a king or a heart”, so the cards that are a king or a heart are counted first. The king of hearts is in both groups and must be counted only once.
Kings or hearts \(=4+13-1=16\) cards
Neither a king nor a heart \(=52-16=36\) cards
Probability \(\displaystyle=\frac{36}{52}=\frac{9}{13}\)
Tip: Forgetting the king of hearts gives \(52-17=35\) cards, the \(\frac{35}{52}\) of Option (3).