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

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