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

20%?

Explanation:

Answer 2

Option A - 17%

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=(60)/(360)*\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}=(A_s)/(A)`

`\text{Probability}=((60)/(360)*\pi r^2)/(\pi r^2)`

`\text{Probability}=(60)/(360)`

`\text{Probability}=(1)/(6)`

`\text{Probability}=0.1666`

Into percentage, P=16.66% ≈ 17%.

Therefore, Option A is correct.