Question

A target with a diameter of 28 cm has 4 scoring zones formed by concentric circles. The diameter of the center circle is 4 cm. The width of each ring is 4 cm. A dart hits the target at a random point. Find the probability that it will hit a point in the yellow region.

Answer 1

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) :

⇒ $P =\frac{area\ of\ the\ yellow\ zone}{area\ of\ the\ entire\ target}$

So,

Lets find the area of the yellow zone;

⇒ Area (yellow zone), $A_y$ = Area of yellow circle - Area of the black circle

⇒ $A_y = Area\ (yellow\ circle)-Area\ (center\ circle)$

⇒ $A_y= \pi R^2-\pi r^2$

⇒ $A_y= \pi (R^2- r^2)$

⇒ $A_y = \pi (6^2- 2^2)$

⇒ $A_y= \pi (36- 4)$

⇒ $A_y = \pi (32)$ cm^2

Now,

⇒ Area of the entire target, A1:

⇒ $A_1=\pi (R_1)^2$

⇒ $A_1=\pi (14)^2$               ...R1=14 cm

⇒ $A_1=\pi (196)$ cm^2

Probability:

⇒ $P=\frac{A_y}{A_1}$

⇒ $P=\frac{\pi (32) }{\pi (196)}$

⇒ $P=\frac{32 }{196}$

⇒ $P=0.16$

In terms of percentage it is $0.16\times 100=16\%$

The probability of a dart hitting the target in the yellow zone is 0.16 or 16% .