document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193192>Question 1193192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
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document.write( "Standard dartboard dimensions:\r<BR>\n" );
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document.write( "The Double/Inner Bull inside radius (inner red circle) = 6.35 mm.\r<BR>\n" );
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document.write( "The radius of the Single/Outer Bull (outer green ring), from the centre to outer edge = 15.9 mm.\r<BR>\n" );
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document.write( "The radius of the Treble Area/Inner Ring, from the centre to outer edge = 107 mm.\r<BR>\n" );
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document.write( "The radius of the Double Area/Outer Ring, from the centre to outer edge = 170 mm.\r<BR>\n" );
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document.write( "Width of Double Area/Outer Ring and Treble Area/Inner Ring = 8 mm\r<BR>\n" );
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document.write( "1.) Sketch a dartboard and properly dimension. Calculate the areas of:\r<BR>\n" );
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document.write( "Double Area/Outer Ring<BR>\n" );
document.write( "Treble Area/Inner Ring<BR>\n" );
document.write( "Normal point value area.\r<BR>\n" );
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document.write( "QUESTION:\r<BR>\n" );
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document.write( "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?\r<BR>\n" );
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document.write( "2.Use the areas that you calculated for the previous question.<BR>\n" );
document.write( "If you threw a dart randomly and it landed on the board for points, what is the probability that it would be worth 28?\r<BR>\n" );
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document.write( "3.Use the areas that you calculated for the previous question.<BR>\n" );
document.write( "If you threw a dart randomly and it landed on the board for points, what is the probability that it would be worth 6?\r<BR>\n" );
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document.write( "4.Use the areas that you calculated for the previous question.<BR>\n" );
document.write( "If you threw a dart randomly and it landed on the board for points, what is the probability that it would be worth 10? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848853 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Sketch and Calculate Areas**\r<BR>\n" );
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document.write( "* **Sketch:**<BR>\n" );
document.write( "    * Draw a circle representing the dartboard.<BR>\n" );
document.write( "    * Inside, draw concentric circles to represent the Bull, Treble Ring, Double Ring, and the outer boundary.<BR>\n" );
document.write( "    * Label the radii of each circle as provided.\r<BR>\n" );
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document.write( "* **Calculate Areas:**\r<BR>\n" );
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document.write( "    * **Double Area/Outer Ring:**<BR>\n" );
document.write( "        * Radius of Outer Circle (Double Ring): 170 mm<BR>\n" );
document.write( "        * Radius of Inner Circle (Treble Ring): 170 mm - 8 mm = 162 mm<BR>\n" );
document.write( "        * Area of Outer Ring = π(R² - r²) = π(170² - 162²) ≈ 8796.46 mm²\r<BR>\n" );
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document.write( "    * **Treble Area/Inner Ring:**<BR>\n" );
document.write( "        * Radius of Outer Circle (Treble Ring): 107 mm<BR>\n" );
document.write( "        * Radius of Inner Circle (Double Bull): 107 mm - 8 mm = 99 mm<BR>\n" );
document.write( "        * Area of Inner Ring = π(R² - r²) = π(107² - 99²) ≈ 5277.88 mm²\r<BR>\n" );
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document.write( "    * **Normal Point Value Area:**<BR>\n" );
document.write( "        * 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)<BR>\n" );
document.write( "        * Radius of Inner Circle (Treble Ring): 107 mm<BR>\n" );
document.write( "        * Area of Normal Point Value Area = π(R² - r²) = π(200² - 107²) ≈ 27566.37 mm²\r<BR>\n" );
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document.write( "**2. Probability of Landing on a 5**\r<BR>\n" );
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document.write( "* To score 5, the dart must land in the normal scoring area.<BR>\n" );
document.write( "* **Probability = (Area of Normal Point Value Area) / (Total Area of the Dartboard)** <BR>\n" );
document.write( "* Probability = 27566.37 mm² / (Assuming a dartboard radius of 200 mm, Total Area = π * 200² = 125663.71 mm²)<BR>\n" );
document.write( "* Probability ≈ 0.219 <BR>\n" );
document.write( "* **Therefore, the probability of landing on a 5 is approximately 0.219 or 21.9%.**\r<BR>\n" );
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document.write( "**3. Probability of Landing on a 28**\r<BR>\n" );
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document.write( "* To score 28, the dart must land in the double ring of a 14.<BR>\n" );
document.write( "* **Probability = (Area of Double Ring) / (Total Area of the Dartboard)**<BR>\n" );
document.write( "* Probability = 8796.46 mm² / 125663.71 mm² <BR>\n" );
document.write( "* Probability ≈ 0.070 <BR>\n" );
document.write( "* **Therefore, the probability of landing on a 28 is approximately 0.070 or 7.0%.**\r<BR>\n" );
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document.write( "**4. Probability of Landing on a 6**\r<BR>\n" );
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document.write( "* To score 6, the dart must land in the treble ring of a 2.<BR>\n" );
document.write( "* **Probability = (Area of Treble Ring) / (Total Area of the Dartboard)**<BR>\n" );
document.write( "* Probability = 5277.88 mm² / 125663.71 mm² <BR>\n" );
document.write( "* Probability ≈ 0.042 <BR>\n" );
document.write( "* **Therefore, the probability of landing on a 6 is approximately 0.042 or 4.2%.**\r<BR>\n" );
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document.write( "**5. Probability of Landing on a 10**\r<BR>\n" );
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document.write( "* To score 10, the dart must land in the normal scoring area of a 10.<BR>\n" );
document.write( "* **Probability = (Area of Normal Point Value Area) / (Total Area of the Dartboard)**<BR>\n" );
document.write( "* Probability = 27566.37 mm² / 125663.71 mm² <BR>\n" );
document.write( "* Probability ≈ 0.219 <BR>\n" );
document.write( "* **Therefore, the probability of landing on a 10 is approximately 0.219 or 21.9%.**\r<BR>\n" );
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document.write( "**Important Notes:**\r<BR>\n" );
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document.write( "* These probabilities are based on the assumption of a perfectly random throw, which is not always the case in reality. <BR>\n" );
document.write( "* The actual probabilities may vary depending on the skill level of the player.<BR>\n" );
document.write( "* The assumed dartboard radius of 200 mm may not be accurate for all standard dartboards. \r<BR>\n" );
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document.write( "I hope this helps! Let me know if you have any further questions.<BR>\n" );
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