Ctrl+k

Find probabilities from cards

Probability from cards is determined by identifying the equally likely outcomes in the deck and comparing the number of cards with the desired property—such as a color, suit, rank, or number—to the total number of cards: P(event)=favorable outcomestotal outcomesP(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}. The probability can be represented as a fraction, decimal, or percent and interpreted from 0 to 1; this scope concerns straightforward single-draw situations, not advanced dependent or conditional probability.

Detailed Explanation: Find probabilities from cards

When drawing one card from a standard deck, each card is equally likely to be chosen. To find a probability:

P(event)=number of favorable cardstotal number of cardsP(\text{event})=\frac{\text{number of favorable cards}}{\text{total number of cards}}

Example

What is the probability of drawing a heart from a standard 52-card deck?

  1. Find the total number of cards.
    A standard deck has 5252 cards.

  2. Count the favorable cards.
    There are 1313 hearts in the deck.

  3. Write the probability.

P(heart)=1352 P(\text{heart})=\frac{13}{52}

  1. Simplify the fraction.
    Divide the numerator and denominator by 1313:

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

So, the probability of drawing a heart is:

14\boxed{\frac{1}{4}}

This is also 0.250.25 or 25%25\%.

Learn by doing: Find probabilities from cards

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Probability - Cards, From Hand, Pick One of Group, To Percent

      ?