SOLUTION: Five concentric circles with radii 1, 2, 3, 4, and 5 are drawn as shown dividing the circle of radius 5 into five regions: a circle of radius 1 and 4 annuuli (rings). What is the p

Algebra ->  Probability-and-statistics -> SOLUTION: Five concentric circles with radii 1, 2, 3, 4, and 5 are drawn as shown dividing the circle of radius 5 into five regions: a circle of radius 1 and 4 annuuli (rings). What is the p      Log On


   

Question 907049: Five concentric circles with radii 1, 2, 3, 4, and 5 are drawn as shown dividing the circle of radius 5 into five regions: a circle of radius 1 and 4 annuuli (rings). What is the probability that a point chosen randomly from within the circle of radius 5 lies in the annulus whose inner radius is 3 and who outer radius is 4?
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Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the areas for each of the 5 regions.
A%5B1%5D=pi%281%29%5E2=3.14
A%5B2%5D=pi%282%29%5E2-pi%281%29%5E2=9.42
A%5B3%5D=pi%283%29%5E2-pi%282%29%5E2=15.71
A%5B4%5D=pi%284%29%5E2-pi%283%29%5E2=21.99
A%5B5%5D=pi%285%29%5E2-pi%284%29%5E2=28.27
The total area is A%5Btot%5D=pi%285%5E2%29=78.54
The probability of being in each region is proportional to the area of the region divided by the area of the entire region.
P%5B1%5D=3.14%2F78.54=0.04
P%5B2%5D=9.42%2F78.54=0.12
P%5B3%5D=15.71%2F78.54=0.20
P%5B4%5D=21.99%2F78.54=highlight%280.28%29
P%5B5%5D=28.27%2F78.54=0.36