## 289. Math Puzzle 6/89

Skat. Not an unsophisticated game that provides fun and challenges the mind. In the game, two cards are now laid out one after the other, blind.

Based on the relative frequency of the cards, you should calculate the probability that the first card is a King and the second card is an Ace.

How many times can this case occur if a Skat tournament with a total of 1000 rounds is assumed?
Due to the relative frequencies, the probabilities are

$$
p_{\text {King }}=\frac{4}{32}=0.125 \quad, \quad p_{\text{Ace}}=\frac{4}{31}=0.129
$$

From this, the probability that the first card is a King and the second card is an Ace is as follows:

$$
p=p_{\text {King }} \cdot p_{\text{Ace}}=0.125 \cdot 0.129=0.016
$$

In a tournament of 1000 games, the case of "King/Ace" as the first and second card can only occur 16 times.