These questions are based on a 52 cards deck without Jokers. 1. Find the probability of drawing cards 3 through 7 . 2. Find the probability of drawing a face card that is red. -_ robability on Numbers

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Let's tackle each question one by one based on a standard 52-card deck without Jokers.

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### **1. Probability of Drawing Cards 3 Through 7**

**Understanding the Problem:**
- **Cards 3 through 7** refer to the ranks **3, 4, 5, 6, and 7** in each of the four suits (Hearts, Diamonds, Clubs, Spades).
- Each rank has **4 cards** (one in each suit).

**Calculating the Probability:**
1. **Total favorable cards:**
   - There are **5 ranks** (3, 4, 5, 6, 7).
   - Each rank has **4 cards**.
   - So, total favorable cards = 5 ranks × 4 suits = **20 cards**.

2. **Total possible cards:**
   - A standard deck has **52 cards**.

3. **Probability Formula:**
   $$
   \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{20}{52}
   $$

4. **Simplifying the Fraction:**
   $$
   \frac{20}{52} = \frac{5}{13} \approx 0.3846 \text{ or } 38.46\%
   $$

**Answer:**  
The probability of drawing a card ranked 3 through 7 is **$$\frac{5}{13}$$ or approximately 38.46%**.

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### **2. Probability of Drawing a Red Face Card**

**Understanding the Problem:**
- **Face cards** include **Jacks, Queens, and Kings**.
- There are **4 suits**: Hearts and Diamonds are **red**, while Clubs and Spades are **black**.
- Each suit has **3 face cards** (Jack, Queen, King).

**Calculating the Probability:**
1. **Total face cards:**
   - 3 face cards per suit × 4 suits = **12 face cards**.

2. **Total red face cards:**
   - Since Hearts and Diamonds are red, and each has 3 face cards:
   - 3 face cards per red suit × 2 red suits = **6 red face cards**.

3. **Total possible cards:**
   - A standard deck has **52 cards**.

4. **Probability Formula:**
   $$
   \text{Probability} = \frac{\text{Number of red face cards}}{\text{Total number of possible cards}} = \frac{6}{52}
   $$

5. **Simplifying the Fraction:**
   $$
   \frac{6}{52} = \frac{3}{26} \approx 0.1154 \text{ or } 11.54\%
   $$

**Answer:**  
The probability of drawing a red face card is **$$\frac{3}{26}$$ or approximately 11.54%**.

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### **Summary**

1. **Probability of drawing a card ranked 3 through 7:** $$\frac{5}{13}$$ (~38.46%)
2. **Probability of drawing a red face card:** $$\frac{3}{26}$$ (~11.54%)

If you have any further questions or need additional clarifications, feel free to ask!
The probability of drawing a card ranked 3 through 7 is 5/13 (approximately 38.46%). The probability of drawing a red face card is 3/26 (approximately 11.54%).

These questions are based on a 52 cards deck without Jokers. 1. Find the probability of drawing cards 3 through 7 . 2. Find the probability of drawing a face card that is red. -_ robability on Numbers

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