Answer
18
Work Step by Step
Cards are drawn at random from a deck
and replaced after each draw. Find the average number of
cards that would be drawn to get 4 face cards.
The probability of getting a face card from a deck is $p=\frac{12}{52}=\frac{3}{13}$
Set $k=4$ and use the negative binomial distribution formula, we have
$\mu=\frac{k}{p}=4\times\frac{13}{3}=17.33$
Thus, the average number of cards that would be drawn to get 4 face cards is 17.33 (round up to 18).
