Answer :
To determine the probability of drawing a '6' from a standard deck of cards, you need to perform the following steps:
1. Understand the Structure of a Deck:
- A standard deck consists of 52 cards.
- There are 4 suits in the deck: Hearts, Clubs, Diamonds, and Spades.
- Each suit contains 13 cards: numbers 2 through 10, and the face cards Jack (J), Queen (Q), King (K), as well as an Ace (A).
2. Identify the Number of '6' Cards:
- Each suit has one '6' card.
- Since there are 4 suits, and each suit has one '6', there are a total of 4 '6' cards in the deck.
3. Calculate the Probability:
- Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
- The number of favorable outcomes in this case is the number of '6' cards, which is 4.
- The total number of possible outcomes is the total number of cards in the deck, which is 52.
4. Formulate the Probability:
- The probability of drawing a '6' can be expressed mathematically as:
[tex]\[ \text{Probability} = \frac{\text{Number of '6' cards}}{\text{Total number of cards}} = \frac{4}{52} \][/tex]
5. Simplify the Fraction (If Necessary):
- The fraction [tex]\(\frac{4}{52}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[ \frac{4}{52} = \frac{4 \div 4}{52 \div 4} = \frac{1}{13} \][/tex]
6. Convert to Decimal (If Desired):
- To convert the fraction to a decimal form, you can divide the numerator by the denominator:
[tex]\[ \frac{1}{13} \approx 0.0769 \][/tex]
So, the probability of drawing a '6' from a standard deck of cards is approximately [tex]\(0.0769\)[/tex], which confirms that [tex]\(\frac{4}{52}\)[/tex] is the correct and simplified form of the probability of drawing a '6'.
Therefore, the answer to the question is:
[tex]\[ \frac{4}{52} \approx 0.0769 \][/tex]
1. Understand the Structure of a Deck:
- A standard deck consists of 52 cards.
- There are 4 suits in the deck: Hearts, Clubs, Diamonds, and Spades.
- Each suit contains 13 cards: numbers 2 through 10, and the face cards Jack (J), Queen (Q), King (K), as well as an Ace (A).
2. Identify the Number of '6' Cards:
- Each suit has one '6' card.
- Since there are 4 suits, and each suit has one '6', there are a total of 4 '6' cards in the deck.
3. Calculate the Probability:
- Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
- The number of favorable outcomes in this case is the number of '6' cards, which is 4.
- The total number of possible outcomes is the total number of cards in the deck, which is 52.
4. Formulate the Probability:
- The probability of drawing a '6' can be expressed mathematically as:
[tex]\[ \text{Probability} = \frac{\text{Number of '6' cards}}{\text{Total number of cards}} = \frac{4}{52} \][/tex]
5. Simplify the Fraction (If Necessary):
- The fraction [tex]\(\frac{4}{52}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[ \frac{4}{52} = \frac{4 \div 4}{52 \div 4} = \frac{1}{13} \][/tex]
6. Convert to Decimal (If Desired):
- To convert the fraction to a decimal form, you can divide the numerator by the denominator:
[tex]\[ \frac{1}{13} \approx 0.0769 \][/tex]
So, the probability of drawing a '6' from a standard deck of cards is approximately [tex]\(0.0769\)[/tex], which confirms that [tex]\(\frac{4}{52}\)[/tex] is the correct and simplified form of the probability of drawing a '6'.
Therefore, the answer to the question is:
[tex]\[ \frac{4}{52} \approx 0.0769 \][/tex]
