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:

$\frac{4}{13}$

The correct answer is Option (4) → $\frac{4}{13}$

Note: The given answer is as per NTA answer key. However, there is an ambiguity in the question and the answer should be 15/52 which is not there in any of the options as explained below.

The phrase: “either a Queen or a Spade (but not both)” represents an exclusive OR condition, meaning:

• Queens excluding the Queen of Spades, and
• Spades excluding the Queen of Spades.

Therefore: 

• Other Queens = 4−1=3
• Other Spades = 13−1=12

Total Favourable outcomes: 3 + 12 = 15

So, if the wording “but not both” is interpreted strictly, then P = 15/52.

The option 4/13 comes from: $P(Q \cup S) = P(Q) + P(S) - P(Q \cap S) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$ 

which corresponds to: “Queen or Spade” including the Queen of Spades.

Therefore, the question contains a contradiction:

• the wording suggests exclusive OR,
• but the options suggest the examiner intended the standard inclusive OR.