Question

If 2 cards are selected from a standard deck of cards. The first card is placed back in the deck before the second card is drawn. Find the following probabilities:

a) P (Heart and club)

d) P (2 Aces)

b) P (Red card and 4 of spades)

e) P (Queen of hearts and King)

c) P (Spade and Ace of hearts)

f) P (2 of the same card)

20) Find the same probabilities for problem #19 but this time, the card is not placed back in the deck before the 2nd card is drawn. 

Answer 1

1.

a)

$P=\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{16}$

d)

$P=\frac{1}{13}\cdot\frac{1}{13}=\frac{1}{169}$

b)

$P=\frac{1}{2}\cdot\frac{1}{52}=\frac{1}{104}$

e)

$P=\frac{1}{52}\cdot\frac{1}{13}=\frac{1}{676}$

c)

$P=\frac{1}{4}\cdot\frac{1}{52}=\frac{1}{208}$

f)

$P=\frac{1}{52}\cdot\frac{1}{52}=\frac{1}{2704}$

2.

a)

$P=\frac{1}{4}\cdot\frac{13}{51}=\frac{13}{204}$

d)

$P=\frac{1}{13}\cdot\frac{3}{51}=\frac{1}{221}$

b)

$P=\frac{1}{2}\cdot\frac{1}{51}=\frac{1}{102}$

e)

$P=\frac{1}{52}\cdot\frac{4}{51}=\frac{1}{663}$

c)

$P=\frac{1}{4}\cdot\frac{1}{51}=\frac{1}{204}$

f)

$P=0$