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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

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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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