Question

Suppose you have two packs each of 52 playing cards. A card is drawn from the first and a card is drawn from the second. What is the probability that
a) both cards are diamond?
b) both cards are black?
c) both cards are Kings?

Answer 1

a)There are 13 diamond cards in one deck, then the probability is

$\frac{13}{52}\cdot\frac{13}{52}=\frac{1}{16}$

b)There are 26 black cards in one deck, then the probability is

$\frac{26}{52}\cdot\frac{26}{52}=\frac{1}{4}$

c)There are 4 Kings cards in one deck, then the probability is

$\frac{4}{52}\cdot\frac{4}{52}=\frac{1}{169}$