Answer
$P(card~1~is~king~and~card~2~is~king)=\frac{1}{169}=0.005917$
Work Step by Step
If the sampling is done with replacement, the events are independent.
- The first card:
The sample space: 52 cards from a standard 52-card deck. So, $N(S_1)=52$
There are 4 kings. So, $N(card~1~is~king)=4$
Using the Classical Method (page 259):
$P(card~1~is~king)=\frac{N(card~1~is~king)}{N(S_1)}=\frac{4}{52}=\frac{1}{13}$
- The second card:
The sample space: 52 cards from a standard 52-card deck. So, $N(S_2)=52$
There are 4 kings. So, $N(card~2~is~king)=4$
Using the Classical Method (page 259):
$P(card~2~is~king)=\frac{N(card~2~is~king)}{N(S_2)}=\frac{4}{52}=\frac{1}{13}$
Now, using the Multiplication Rule for Independent Events (page 282):
$P(card~1~is~king~and~card~2~is~king)=P(card~1~is~king)\times P(card~2~is~king)=\frac{1}{13}\times\frac{1}{13}=\frac{1}{169}=0.005917$
