A card is drawn at random from a well-shuffled pack of 52. Which of the following pairs of events is independent?

Explanation

1. 01

   Spade and ace: only the ace of spades is both, $\frac{1}{52}$, and $\frac{13}{52} \times \frac{4}{52} = \frac{1}{52}$: independent.

2. 02

   The rest fail: spade and black give $\frac{13}{52} \ne \frac{13}{52} \times \frac{26}{52}$; a king and an ace cannot happen together; heart and red ace give $\frac{1}{52} \ne \frac{13}{52} \times \frac{2}{52}$.