# Deck of Cards Probability Calculator

**Created By :** Vaibhavi Kumari

**Reviewed By :** Phani Ponnapalli

**Last Updated :** Mar 21, 2023

Take advantage of this free Cumulative Probability Calculator tool to compute the chances of occurring two or more events. We can use this calculator by entering the inputs in the below input fields and gently tap the calculate button to get the answers quickly.

### How to Calculate the Probability of Cards ?

Usually, when you are drawing cards, you want to know your odds you need to use something called hypergeometric distribution, i.e. finding probability of cards. Let us use the formula to find the probability of cards.

**H (n) = C (X, n) * C (Y – X, Z – n) / C (Y, Z)**

Where,

X is the no. of a certain card in the deck.

Y is the total no. of cards in the deck.

Z is the no. of cards drawn

N is the number that you are checking for.

### Deck of Cards Probability with Steps

By adhering to the steps which are shown below, you can calculate the probability of cards very easily.

- Step 1: Note down all the cards which are possible and mark the ones that you would drag out.
- Step 2: Count the total number of cards in the deck(s).
- Step 3: Write the answer as a fraction. That's all you will get the answer.

### Deck of Cards Probability Example Question

**Example Question 1: If you have a standard 52 card deck and draw 4 cards, what will be your chances of drawing an ace? As, X is 4, Y is 52, Z is 4, N is 1 .**

**Solution:**

From the given input data X = 4, Y = 52, Z = 4, N = 1

As, we know the formula, H (n) = C (X, n) * C (Y – X, Z – n) / C (Y, Z)

Substitute the values in the formula and the equation becomes

H (n) = C (4, 1) * C (52 – 4, 4 – 1) / C (52, 4)

H (n) = 4 * 1712304 /270725

H (n) = 6849216 /270725.

**Example Question 2: Find the probability of a club in a deck of cards?**

**Solution:**

Normally, we all know the deck of cards is

- 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

Here, we need to find club

Clubs: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A = total = 13

The total number of cards in a deck is 52

Probability = No. of favorable outcomes / Total no. of outcomes.

Now, the probability of cards in a deck is 13/52.

Understand different concepts and get good grip on them by using online tools available at probabilitycalculator.guru and clarify your concerns.

### FAQs on Deck of Cards Probability Calculator

**1. How to use the deck of cards probability calculator?**

All you need to do is give the inputs in the input fields and click on the calculate button and get the answers instantaneously.

**2. How do you calculate the probability of cards in a deck?**

Probability of cards can be calculated by the formula, H (n) = C (X, n) * C (Y – X, Z – n) / C (Y, Z)

**3. What is the best tool to find the probability of cards in a deck(s)?**

Deck of Cards Probability calculator is the best tool to find the probability of cards , which is available at probabilitycalculator.guru