Question 1193192
**1. Sketch and Calculate Areas**

* **Sketch:**
    * Draw a circle representing the dartboard.
    * Inside, draw concentric circles to represent the Bull, Treble Ring, Double Ring, and the outer boundary.
    * Label the radii of each circle as provided.

* **Calculate Areas:**

    * **Double Area/Outer Ring:**
        * Radius of Outer Circle (Double Ring): 170 mm
        * Radius of Inner Circle (Treble Ring): 170 mm - 8 mm = 162 mm
        * Area of Outer Ring = π(R² - r²) = π(170² - 162²) ≈ 8796.46 mm²

    * **Treble Area/Inner Ring:**
        * Radius of Outer Circle (Treble Ring): 107 mm
        * Radius of Inner Circle (Double Bull): 107 mm - 8 mm = 99 mm
        * Area of Inner Ring = π(R² - r²) = π(107² - 99²) ≈ 5277.88 mm²

    * **Normal Point Value Area:**
        * Radius of Outer Circle (Entire Board): Assume a reasonable radius for the entire board (e.g., 200 mm - this may vary depending on the actual dartboard size)
        * Radius of Inner Circle (Treble Ring): 107 mm
        * Area of Normal Point Value Area = π(R² - r²) = π(200² - 107²) ≈ 27566.37 mm²

**2. Probability of Landing on a 5**

* To score 5, the dart must land in the normal scoring area.
* **Probability = (Area of Normal Point Value Area) / (Total Area of the Dartboard)** 
* Probability = 27566.37 mm² / (Assuming a dartboard radius of 200 mm, Total Area = π * 200² = 125663.71 mm²)
* Probability ≈ 0.219 
* **Therefore, the probability of landing on a 5 is approximately 0.219 or 21.9%.**

**3. Probability of Landing on a 28**

* To score 28, the dart must land in the double ring of a 14.
* **Probability = (Area of Double Ring) / (Total Area of the Dartboard)**
* Probability = 8796.46 mm² / 125663.71 mm² 
* Probability ≈ 0.070 
* **Therefore, the probability of landing on a 28 is approximately 0.070 or 7.0%.**

**4. Probability of Landing on a 6**

* To score 6, the dart must land in the treble ring of a 2.
* **Probability = (Area of Treble Ring) / (Total Area of the Dartboard)**
* Probability = 5277.88 mm² / 125663.71 mm² 
* Probability ≈ 0.042 
* **Therefore, the probability of landing on a 6 is approximately 0.042 or 4.2%.**

**5. Probability of Landing on a 10**

* To score 10, the dart must land in the normal scoring area of a 10.
* **Probability = (Area of Normal Point Value Area) / (Total Area of the Dartboard)**
* Probability = 27566.37 mm² / 125663.71 mm² 
* Probability ≈ 0.219 
* **Therefore, the probability of landing on a 10 is approximately 0.219 or 21.9%.**

**Important Notes:**

* These probabilities are based on the assumption of a perfectly random throw, which is not always the case in reality. 
* The actual probabilities may vary depending on the skill level of the player.
* The assumed dartboard radius of 200 mm may not be accurate for all standard dartboards. 

I hope this helps! Let me know if you have any further questions.