EZ Math

Statistics · Probability

How to Find the Probability of Drawing a Heart

Problem

a heart from a standard deck\text{a heart from a standard deck}

Answer

14\frac{1}{4}

A standard deck has 52 cards: four suits of 13. Count the cards you want, divide by 52, then reduce the fraction.

Step-by-step solution

  1. Count the total number of cards.

    52 cards52\ \text{cards}

    Why: A standard deck has four suits with 13 cards each.

  2. Count the hearts.

    13 hearts13\ \text{hearts}

    Why: One of the four suits is hearts, and each suit has 13 cards.

  3. Divide and simplify.

    1352=14\frac{13}{52} = \frac{1}{4}

    Why: Thirteen divides both numbers, leaving one over four.

Common mistakes

  • Using 51 as the denominator. That counts the second card drawn without replacement.
  • Counting the whole suit and forgetting to simplify 13 over 52.
  • Using 13 over 4 or 4 over 52 instead of 13 over 52.

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 red card\text{a red card}

    Show answer

    12\frac{1}{2}

  3. a face card\text{a face card}

    Show answer

    313\frac{3}{13}

  4. a club\text{a club}

    Show answer

    14\frac{1}{4}

  5. not a heart\text{not a heart}

    Show answer

    34\frac{3}{4}