SOLUTION: A target consists of concentric circles of radii 1 cm, 2 cm and 3 cm. The innermost circle is colored red, the middle ring is colored white, and the outer ring is colored blue. If

Algebra ->  Probability-and-statistics -> SOLUTION: A target consists of concentric circles of radii 1 cm, 2 cm and 3 cm. The innermost circle is colored red, the middle ring is colored white, and the outer ring is colored blue. If       Log On


   

Question 316472: A target consists of concentric circles of radii 1 cm, 2 cm and 3 cm. The innermost circle is colored red, the middle ring is colored white, and the outer ring is colored blue. If a point is chosen at random on the target, what is the probability that it lies in the blue region? Express your answer as a common fraction.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Calculate the areas of each region.
The total target area is,
Atot=pi%2A3%5E2=9%2Api
Ar=pi%2A1%5E2=pi
Aw=pi%2A2%5E2-pi%2A1%5E2=%284-1%29%2Api=3%2Api
Ab=pi%2A3%5E2-pi%2A2%5E2=%289-4%29%2Api=5%2Api
The probabilities for each color is determined by the amount of area in each region compared to the total area.
P%28R%29=%28pi%29%2F%289%2Api%29=1%2F9
P%28W%29=%283%2Api%29%2F%289%2Api%29=3%2F9=1%2F3
P%28B%29=%285%2Api%29%2F%289%2Api%29=5%2F9
So, the probability of a blue region pick is 5/9.