Question 95587This question is from textbook Prentice Hall Algebra 2
: I am trying to help my grandson with his Algebra homework. I guess I have forgotten much of what I knew at one time. I appreciate any help you can give me on this problem.
Suppose that a dart lands at random on the dartboard shown at the right. Find each theoretical probablility.
17. The dart lands in the bull's eye
18. The dart lands in a green region
19. The dart scores at least 10 points
20. The dart scores less than 10 points.
The dart board shows: r= 1.5 in Width of each ring = 1.5 in.
Bulls eye is 20 points, next ring is 10 points, next 5 points, outside ring 2 points.
Thank you so much.
This question is from textbook Prentice Hall Algebra 2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose that a dart lands at random on the dartboard shown at the right. Find each theoretical probablility.
17. The dart lands in the bull's eye
18. The dart lands in a green region
19. The dart scores at least 10 points
20. The dart scores less than 10 points.
The dart board shows: r= 1.5 in Width of each ring = 1.5 in.
Bulls eye is 20 points, next ring is 10 points, next 5 points, outside ring 2 points.
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To find the theoretical probabilities it is necessary to determine
the area of of the center, each ring and the whole board.
For example:
If I read your dimensions correctly, the radius of the board is 6 inches
The total area of the board is 6^2pi = 36pi sq. in.
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Area of the "2" ring is 6^2pi-4.5^2pi = (36-20.25)pi = 15.75pi sq. in.
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Area of the "5" ring is 4.5^2pi - 3^2pi = (20.25-9)pi = 11.25pi sq in
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Area of the 10 ring is 3^2pi-1.5^2pi = (9-2.25)pi = 6.75pi sq in
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Area of the bull's eye = 1.5^2pi = 2.25pi sq. in.
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Now you can figure out the probabilities:
17. The dart lands in the bull's eye
P(bull's eye) = 2.25pi/36pi = 0.0625
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18. The dart lands in a green region
I don't know what the green region area is.
Figure that out and divide by 36pi sq in
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19. The dart scores at least 10 points
P(10 area) = 6.75pi/36pi= 0.1875
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20. The dart scores less than 10 points.
P(less than 10) = (2 area + 5 area)/36pi = (15.75+11.25)pi/36pi = 27pi/36pi
= 0.75
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Cheers,
Stan H.
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