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Geometric Probability in Darts: 10 points or 0 points?

When throwing a dart at a square board, the probability of getting 10 points or 0 points can be determined using geometric probability. This example explores the probabilities and provides a guided practice exercise.

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Geometric Probability in Darts: 10 points or 0 points?

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  1. Darts You throw a dart at the square board shown. Your dart is equally likely to hit any point inside the board. Are you more likely to get 10 points or 0 points? Area of smallest circle P(10 Points) = Area of entire board π 32 9π π 0.0873 = = = 182 324 36 EXAMPLE 5 Find a geometric probability SOLUTION

  2. Area outside largest circle P(0 points) = Area of entire board 182 – (π 92) = 182 324 – 81π = 324 4 – π = 4 0.215 Because 0.215 > 0.0873, you are more likely to get 0 points. ANSWER EXAMPLE 5 Find a geometric probability

  3. What If?In Example 5, are you more likely to get 5 points or 0 points? Because 0.2616 > 0.215, you are more likely to get 5 points. ANSWER for Example 5 GUIDED PRACTICE

  4. Area outside largest circle P(0 points) = Area of entire board 182 – (π 92) = 182 324 – 81π = 324 4 – π = 4 0.215 Because 0.2616 > 0.215, you are more likely to get 5 points. ANSWER EXAMPLE 5 Find a geometric probability

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