EZ Math

Statistics · Probability

How to Find the Probability of Drawing a Face Card

Problem

a face card from a 52-card deck\text{a face card from a 52-card deck}

Answer

313\frac{3}{13}

A standard deck has 52 cards in four suits. Probability is favourable outcomes over the 52 total.

Step-by-step solution

  1. Count the face cards.

    3 per suit×4 suits=123\ \text{per suit} \times 4\ \text{suits} = 12

    Why: The face cards are the jack, queen and king.

  2. Count the cards in the deck.

    5252

    Why: A standard deck has 52 cards in total.

  3. Divide and simplify.

    1252=313\frac{12}{52} = \frac{3}{13}

    Why: Divide the top and bottom by the common factor 4.

Common mistakes

  • Counting 16 by including the aces. Aces are not face cards.
  • Using 13 instead of 52 as the total.
  • Stopping at 12/52. Simplify the fraction.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. a king\text{a king}

    Show answer

    113\frac{1}{13}

  2. a spade\text{a spade}

    Show answer

    14\frac{1}{4}

  3. a red card\text{a red card}

    Show answer

    12\frac{1}{2}

  4. an ace\text{an ace}

    Show answer

    113\frac{1}{13}

  5. a number card from 2 to 10\text{a number card from 2 to 10}

    Show answer

    913\frac{9}{13}