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

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

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 =(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=(A_y)/(A_1)`

⇒
`P=(\pi (32) )/(\pi (196))`

⇒
`P=(32 )/(196)`

⇒
`P=0.16`

In terms of percentage it is
`0.16* 100=16\%`

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