We draw one card from each of two Hungarian card decks independently. What is the probability that

a) the two drawn cards are of the same suit?

b) the two drawn cards are of the same rank?

c) the two drawn cards are either of the same suit or of the same rank?

d) the card drawn from the second deck has a higher value than the card drawn from the first deck?

(For the example, see the article "The Elements of Probability Theory" in the current issue.)
a) In the second deck, there are always 8 cards that match the color of the card drawn from the first deck. Given that the number of possible cases is 32, the sought probability is

$$
v_{1}=\frac{8}{12}=\frac{1}{4}(=0.25)
$$

b) Since the number of equivalent cards in the second deck is always 4,

$$
v_{2}=\frac{4}{32}=\frac{1}{8}(=0.125)
$$

c) In this case, the number of favorable cases is $8+4-1$, because there is one card that is both of the same color and of the same value. Therefore,

$$
v_{3}=\frac{11}{32}(\approx 0.344)
$$

d) Considering the values - since each is equally likely $-V_{8}^{i .2}=8^{2}=64$ cases are possible. Out of these, in eight cases the values of the two drawn cards are equal. In the remaining 56 cases, in half of them the first card has the higher value, and in the other half the second card has the higher value. Thus, the number of favorable cases is $56 / 2=28$, and the sought probability is

$$
v_{4}=\frac{28}{64}=\frac{7}{16}(\approx 0.438)
$$

Gergely Krammer (Bp., II., Rákóczi g. II. o. t.)