The probability that a card drawn from a pack of 52 cards will be a spade or a queen, is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{4}{13}\)
For “A or B”, the addition rule is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). The queen of spades is both a spade and a queen, so it would be counted twice if the 13 spades and the 4 queens were just added; it is therefore subtracted once.
A pack has 13 spades, so \(P(\text{spade})=\frac{13}{52}\)
It has 4 queens, so \(P(\text{queen})=\frac{4}{52}\)
Only the queen of spades is both, so \(P(\text{both})=\frac{1}{52}\)
\(\displaystyle P(\text{spade or queen})=\frac{13+4-1}{52}=\frac{16}{52}=\frac{4}{13}\)