Question

A normal deck of 52 cards includes 4 suits where each suit ranges from 2 though 10 inclusive, Jack, Queen, King and Ace. In a standard deck of 52 cards laying face down, if you select one card from the pile, what is the probability you select a diamond and a face card (jack, queen or king)?

Answer 1

Answer: 3/52 (~5.77%)

Explanation:

What we know:

• There is a deck of 52 total cards
• These are split into 4 suits
• Each suit contains cards of 2-10, and a Jack, Queen, King, and Ace

How to solve:

  We need to find the probability of drawing one of 3 diamond face cards, which gives us all of the information we need. Using division, we can create a 'x amount of diamond face cards/y amount of total cards' probability.

Process:

Probability of a diamond  face card

Where P is the probability of drawing that card, x is the number of diamond face cards, and y is the total amount of cards.

Set up equation                                                     P = x/y

Substitute                                                               P = (3)/(52)

Answer: 3/52 (~5.77%)

Because there are 3 diamond face cards in the deck, the chance of drawing one is {3 cards out of 52 total}, which is 3/52.

The chance of drawing ANY face card is {(3 per suit, 4 suits=) 12 cards out of 52 total} 12/52 (~23.08%),

The chance of drawing ANY diamond card is {1 suit out of 4 suits} 1/4 (25%)