Answer:
The probability of a dart hitting the target in the yellow zone is 0.16 or 16% .
Step-by-step explanation:
Given:
Four concentric circles.
Radius of center circle, r = 4/2 = 2 cm
Radius of the yellow circle, R = 2+4 =6 cm
We have to find the probability that it will hit a point in the yellow region.
Formula to be used:
Probability (P) :
⇒ [tex]P =\frac{area\ of\ the\ yellow\ zone}{area\ of\ the\ entire\ target}[/tex]
So,
Lets find the area of the yellow zone;
⇒ Area (yellow zone), [tex]A_y[/tex] = Area of yellow circle - Area of the black circle
⇒ [tex]A_y = Area\ (yellow\ circle)-Area\ (center\ circle)[/tex]
⇒ [tex]A_y= \pi R^2-\pi r^2[/tex]
⇒ [tex]A_y= \pi (R^2- r^2)[/tex]
⇒ [tex]A_y = \pi (6^2- 2^2)[/tex]
⇒ [tex]A_y= \pi (36- 4)[/tex]
⇒ [tex]A_y = \pi (32)[/tex] cm^2
Now,
⇒ Area of the entire target, A1:
⇒ [tex]A_1=\pi (R_1)^2[/tex]
⇒ [tex]A_1=\pi (14)^2[/tex] ...R1=14 cm
⇒ [tex]A_1=\pi (196)[/tex] cm^2
Probability:
⇒ [tex]P=\frac{A_y}{A_1}[/tex]
⇒ [tex]P=\frac{\pi (32) }{\pi (196)}[/tex]
⇒ [tex]P=\frac{32 }{196}[/tex]
⇒ [tex]P=0.16[/tex]
In terms of percentage it is [tex]0.16\times 100=16\%[/tex]
The probability of a dart hitting the target in the yellow zone is 0.16 or 16% .
