Question

A dart is thrown at The board shown. it hits the board at a random point. find the probability that it will land in the shaded region. round to the nearest percent.
A. 17%
B.34%
C.20%
D. 25%

Answer 1

Answer:

20%?

Step-by-step explanation:

Answer 2

Answer:

Option A - 17%

Step-by-step explanation:

Given : A dart is thrown at The board shown. it hits the board at a random point.

To find : The probability that it will land in the shaded region. round to the nearest percent?

Solution :

First we find the total area of the circle,

Let r be the radius of the circle

So, Area of the circle is $A=\pi r^2$

Now, Shaded region is with angle 60°.

The area of shaded region is $A_s=\frac{60}{360}\times\pi r^2$      

The probability that dart will land in the shaded region is

$\text{Probability}=\frac{\text{Shaded area}}{\text{Total area}}$      

$\text{Probability}=\frac{A_s}{A}$    

$\text{Probability}=\frac{\frac{60}{360}\times\pi r^2}{\pi r^2}$

$\text{Probability}=\frac{60}{360}$    

$\text{Probability}=\frac{1}{6}$    

$\text{Probability}=0.1666$    

Into percentage, P=16.66% ≈ 17%.

Therefore, Option A is correct.