When a card is drawn from a deck find the probability of getting?

Questions about how to figure out the probability of picking from a deck of cards common in basic stats courses. For example, 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).

Watch the video for examples:

Probability of getting cards from a deck

Watch this video on YouTube.

You might wonder why you’re learning about cards (what’s the point?). The answer is that finding probabilities (like the probability of contracting an illness) can be a tricky concept to grasp at first. So your instructor will try and simplify problems using cards, dice or Bingo numbers. Once you’ve grasped the basics, you’ll start to use “real life” data for probability (usually a bit later on in the class, for example in normal distributions).
Here’s how to find the probability of picking something in a couple of simple steps.

Probability of picking from a deck of cards: 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 or a 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: Write the answer as a fraction. Divide step 3 by Step 4:
  16 / 52

That’s it!

Tip: It isn’t as easy as just adding the number of sevens (4) and the number of clubs (13). 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.

Probability of picking from a deck of cards: Using Excel

Watch the video for an overview and examples of using the hypergeometric distribution in Excel for card probabilities:

Excel Hypergeometric distribution to calculate card probabilities

Watch this video on YouTube.

It gets a LOT more complex if you’re playing a card game, you have a certain number of cards in your hand, and you want to know your odds of getting a certain card if you are drawing a certain number of cards. You have to use something called a hypergeometric distribution to figure out the odds. The formula is: H (n) = C (X, n) * C (Y – X, Z – n) / C (Y, Z) Where: X is the number of a certain card in the deck Y is the total number of cards in the deck Z is the number of cards drawn

N is the number you are checking for