As shown above, a classic deck of cards is made up of 52 cards, 4 suits with clubs and spades black and diamonds and hearts red. There are 13 cards each suit: #2-10, jack, queen, king and ace. Picture (or fa cards are the jack, queen, and king. If you select a card at random, what is the probability of picking a(n) 9 of Diamonds ?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
![### Understanding a Standard Deck of Cards
As shown above, a classic deck of cards is made up of 52 cards. There are 4 suits in total:
- Clubs
- Spades
- Diamonds
- Hearts
Each suit contains 13 cards:
- Numbered cards from 2 to 10
- Three face cards: Jack, Queen, and King
- An Ace
Clubs and Spades are black suited, while Diamonds and Hearts are red suited.
The diagram above visually represents all the cards in a standard deck, sorted by suits in rows:
- The first row displays the Clubs (♣).
- The second row displays the Spades (♠).
- The third row displays the Hearts (♥).
- The fourth row displays the Diamonds (♦).
Each row shows the cards in increasing order starting from Ace (A) to King (K), covering number cards (2-10), and face cards (J for Jack, Q for Queen, and K for King).
### Example Probabilistic Question
**Question:**
If you select a card at random, what is the probability of picking a 9 of Diamonds (♦)?
**Answer:**
To find the probability:
1. **Identify the total number of possible outcomes:** There are 52 cards in total.
2. **Identify the successful outcome:** There is only one 9 of Diamonds in a deck.
Probability is calculated as:
\[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}} \]
Using the numbers:
\[ \text{Probability} = \frac{1}{52} \]
Hence, the probability of picking the 9 of Diamonds at random from a deck of 52 cards is \(\frac{1}{52}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0b6a651-ee36-4dcb-a8eb-1243f21d2006%2F846161d8-e5aa-4929-8c97-5cb21cc1c933%2Fyxktgjb.jpeg&w=3840&q=75)

Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images









