Question

Consider a standard deck of 52 playing cards with 4 suits.

What is the probability of randomly drawing 1 card that is both a red card and a face card?
(Remember that face cards are jacks, queens, and kings.)
Enter your answer as a fraction in simplest form, using the / symbol, like this: 5/14

Answer 1

3/26

Explanation:

In a deck of 52 cards, there are two red suits: Diamonds and Hearts

There are 6 red face cards:

2 red King

2 red Queen

2 red Jack

P(red face card) = 6/52 = 3/26

Answer 2

3/26

Explanation:

The face cards are: Jack, Queen, and King. There are only three face cards for each of the 4 suits.

Among the 4 suits, two of them are red: diamonds and hearts. And, each of these two has 3 faces. That means that in a deck of 52 cards, there are 2 * 3 = 6 cards that are both red cards and face cards.

Probability is (# times specific event can occur) / (# times any general event will occur).

Here, the specific event is drawing a card that is both red and a face card (of which there are 6 ways), and the general event is drawing a card (of which there are 52 ways):

P(draw a card that is both red and a face card) = 6/52 = 3/26