Two cards are drawn together from a pack of 52. What is the probability that one is a spade and the other is a heart?

Given data

• Spades = 13, Hearts = 13.
• Total two-card selections = C(52,2) = 1326.

Concept/ApproachChoose 1 spade and 1 heart: C(13,1) × C(13,1); order does not matter because the draw is simultaneous.

Step-by-step calculationFavourable = 13 × 13 = 169Probability = 169/1326 = 13/102

Verification/AlternativeSequential approach without order: (13/52)×(13/51)×2 = 338/2652 = 169/1326 = 13/102.

Common pitfallsForgetting to treat order properly (double-counting or undercounting).

Final Answer13/102