Question 1193192: The dimensions of a dartboard and its rings are given below. In the game of darts, there are rings in which the score is doubled and tripled.
Standard dartboard dimensions:
The Double/Inner Bull inside radius (inner red circle) = 6.35 mm.
The radius of the Single/Outer Bull (outer green ring), from the centre to outer edge = 15.9 mm.
The radius of the Treble Area/Inner Ring, from the centre to outer edge = 107 mm.
The radius of the Double Area/Outer Ring, from the centre to outer edge = 170 mm.
Width of Double Area/Outer Ring and Treble Area/Inner Ring = 8 mm
1.) Sketch a dartboard and properly dimension. Calculate the areas of:
Double Area/Outer Ring
Treble Area/Inner Ring
Normal point value area.
QUESTION:
1. If you threw a dart randomly and it landed on the board for points, what is the probability that it would be worth 5?
2.Use the areas that you calculated for the previous question.
If you threw a dart randomly and it landed on the board for points, what is the probability that it would be worth 28?
3.Use the areas that you calculated for the previous question.
If you threw a dart randomly and it landed on the board for points, what is the probability that it would be worth 6?
4.Use the areas that you calculated for the previous question.
If you threw a dart randomly and it landed on the board for points, what is the probability that it would be worth 10?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! **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.
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