Geometric probability & archery

Geometry and probability.

Take a look at the target shown. It consists of a circular target with four small squares inside.

If an archer randomly shoots an arrow which hits the target, what is the theoretical probability the arrow will hit the small square on the upper left?

What is the probability that the arrow will hit any one of the four squares?

What is the probability that the arrow will hit the target without hitting any of the four squares?

Comments for Geometric probability & archery

 Jun 28, 2012 Geometric probability & archery by: Staff The answer: If an archer randomly shoots an arrow which hits the target, what is the theoretical probability the arrow will hit the small square on the upper left? Theoretical Probability = # of favorable outcomes / # of total outcomes Theoretical Probability = (area of small square) / (area of circle) Theoretical Probability = (5 * 5) / (pi * 18²) Theoretical Probability = (5 * 5) / (3.14159 * 18²) Theoretical Probability = (25) / (1017.8751600000001) Theoretical Probability = (25) / (1017.88) Theoretical Probability = 0.0246 >>> Theoretical Probability = 2.46% What is the probability that the arrow will hit any one of the four squares? Theoretical Probability = # of favorable outcomes / # of total outcomes Theoretical Probability = 4 * (area of small square) / (area of circle) Theoretical Probability = (4 * 5 * 5) / (pi * 18²) Theoretical Probability = (4 * 5 * 5) / (3.14159 * 18²) Theoretical Probability = (100) / (1017.8751600000001) Theoretical Probability = (100) / (1017.88) Theoretical Probability = 0.0982 >>> Theoretical Probability = 9.82% What is the probability that the arrow will hit the target without hitting any of the four squares? Theoretical Probability = # of favorable outcomes / # of total outcomes Theoretical Probability = [(area of circle) - 4 * (area of small square)] / (area of circle) Theoretical Probability = [(pi * 18²) - 4 * (5 * 5)] / (pi * 18²) Theoretical Probability = [(3.14159 * 18²) - 4 * (5 * 5)] / (3.14159 * 18²) Theoretical Probability = (1017.88 - 100) / (1017.88) Theoretical Probability = (917.88) / (1017.88) Theoretical Probability = 0.9017565921327 >>> Theoretical Probability = 90.02% Thanks for writing. Staff www.solving-math-problems.com

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