Question

In a deck of $50$ cards, there are $5$ face cards. Find the theoretical probability and predict how many face cards would be present in a deck of $120$ cards if the ratio of the face cards to the non-face cards is proportional to the original deck.

Answer 1

The theoretical probability of finding a face card $=\frac{\text{Number of face cards in the deck}}{\text{Total number of cards in the deck}}=\frac{5}{50}=\frac{1}{10}$

Since the ratio of face cards to non-face cards is the same in the deck of $50$ cards and in the deck of $120$ cards, we can use the same theoretical probability to predict how many face cards are present in a deck of $120$ cards.

The number of face cards $=\frac{1}{10}\times 120=12$