From a pack of 52 cards, one card is drawn at random. What is the probability that the card drawn is a ten or a spade?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{4}{13}\)
For “A or B”, the favourable cards of both kinds are counted, but a card that is both is counted only once: \(P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)\). Here the ten of spades is both a ten and a spade.
Tens: 4 cards; spades: 13 cards; ten of spades: 1 card
Cards that are a ten or a spade \(=4+13-1=16\)
Probability \(\displaystyle =\frac{16}{52}=\frac{4}{13}\)
Tip: Adding 4 and 13 without taking away the ten of spades gives \(\frac{17}{52}\), which counts one card twice. In every “or” question, look for the items that belong to both groups.