## 16. Playing Cards

Take any card at random from my deck, and then put it back. Do this three times. You have 19 chances out of 27 to draw at least one face card (king, queen, or jack) this way, because the proportion of face cards in the deck is...

Please complete the last sentence.
16. Let $p$ be the unknown proportion of cards with figures in the deck.

Then the probability of not drawing a card with a figure in one draw from the deck is $1-p$. The probability of not drawing a card with a figure in three draws is $(1-p)^{3}$. In this case, the probability of drawing at least one card with a figure is $1-(1-p)^{3}=19 / 27$. Therefore, $(1-p)^{3}=8 / 27$, i.e., $1-p=2 / 3$.

Thus, $p=1 / 3$, i.e., cards with figures make up $1 / 3$ of the deck.