The probability of the archer hitting the center is the ratio of the area of the center to the area of the target.
1/100, 0.01, or 1 %
Practice makes perfect
An archer takes aim at a target that is 122 centimeters in diameter with 10 concentric circles whose diameters decrease by 12.2 centimeters as they get closer to the center of the target.
To find the probability of the archer hitting the center, we will use geometric probability. To do so, we need to find the ratio of the area of the center and the area of the entire target. Recall the formula for the area of a circle.
A = π r^2
In this formula A is the area of the circle and r is its radius. We know that the diameter of the target is 122 centimeters. Every step closer to the center, the diameter of the circle decreases by 12.2 centimeters. The center is the 9th circle, so the diameter decreased 9 times by 12.2 centimeters each time. Let's calculate the diameter of the center.
Diameter of the Center = 122 - 9* 12.2
⇕
Diameter of the Center = 12.2
The radius of a circle is half of its diameter.
Diameter
Radius
Target
122 cm
61 cm
Center
12.2 cm
6.1 cm
Now we can substitute 61 cm and 6.1 cm into the formula for the area of a circle to find the area of the target and of the center.
A = π r^2 ⇔ lArea of the Center = π (6.1)^2 Area of the Target = π (61)^2
Now let's calculate the probability of the archer hitting the center, which is equal to the ratio of the area of the center and the area of the target.
P(archer hits the center) = Area of the Center/Area of the Target
