How to figure out the probability of picking from a deck of cards in probability and statistics

Probability 6 Comments

Questions about how to figure out the odds of getting certain cards drawn from a deck are common in basic statistics courses. A common question is the probability of choosing one card, and getting a certain number card (e.g. a 7) or one from a certain suit (e.g. a club).  Here’s how to do it in a couple of simple steps.

  • Step 1: figure out the total number of cards you might pull.
    Write down all the possible cards and mark the ones that you would pull out (in our case we’ve been asked the probability of a club ora seven so we’re going to mark all the clubs and all the sevens):

    • hearts: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A
    • clubs: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A
    • spades: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A
    • diamonds: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A

    This totals 16 cards. *

  • Step 2: Count the total number of cards in the deck(s). We have one deck, so the total = 52
  • Step 3: Express the result as a fraction.  Divide step 3 by Step 4:
    16 / 52

That’s it!

* It isn’t as easy as just adding step 1 and step 2. If you did this for this example, you’d get 17 cards, not the correct answer of 16. The reason for this is that one of the cards in our example is both a club AND a number 7.

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  3. How to find the probability of a simple event happening
  4. How to find the probability of selecting a person from a group or committee
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6 Responses to “How to figure out the probability of picking from a deck of cards in probability and statistics”

  1. How to Do Everything Statistics » How to find the probability of a simple event happening said:

    Sep 13, 09 at 5:04 am

    [...] the probability of an event not happening Finding probabilities using frequency distributions Probability of getting certain cards from a deck Probability of selecting a person from a committee or other [...]

  2. Angie Widdows said:

    Sep 17, 09 at 6:20 pm

    this helps make perfect sense. When working problems, I would always come up with the wrong answer. I was not taking into account that one of the cards was 2 of the problems. Now, I understand that you must subtract an extra card in the equation.

  3. Christine Mao said:

    Sep 20, 09 at 8:40 pm

    I was kind of confuse with the deck of cards because I have no idea how many cards were in a deck. The blog was able to break down the cards into suits and that was really helpful in solving the problems.

  4. Lisa Barcomb said:

    Oct 11, 09 at 8:10 pm

    I have the hardest time with this probability for some reason I get lost in the process and then I feel like I am doing it right and come to find out its all wrong every step. this really didn’t help me as this being an example.

  5. card shark said:

    Jul 07, 11 at 1:00 pm

    1 is not a card in the deck

  6. Stephanie said:

    Oct 27, 11 at 9:14 pm

    You are correct! I got carried away typing out all those numbers. Thanks for the correction :)

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