Probability of picking from a deck of cards: Overview
Questions about how to figure out the odds of getting certain cards drawn from a deck are 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).
You might wonder why you’re learning about cards (what’s the point?). The answer is that finding probabilities 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
* 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.