A single card is chosen at random from a standard deck of 52 playing cards. The probability of choosing either a Queen or a Spade (but not both) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{4}{13}\)
Note: The given answer is as per the official NTA Answer Key. However, none of the given options appears to be correct, because the words “but not both” leave out the Queen of Spades, as explained below.
The probability of an event is the number of favourable cards divided by 52. A deck has 4 Queens and 13 Spades, and one card, the Queen of Spades, is both.
A Queen or a Spade but not both: \(3+12=15\) cards, so the probability is \(\displaystyle\frac{15}{52}\), which is not among the options.
The answer given by NTA, \(\frac{4}{13}=\frac{16}{52}\), is the probability of “a Queen or a Spade” with the Queen of Spades counted once: \(4+13-1=16\) cards. The question asked for the Queen of Spades to be left out, but the key quietly let her back in.