Question

- Without looking, Jeff threw a small beanbag on a target with a radius of 20 cm. Adiagram of the target is shown below.10 cm 10 cmcIf the beanbag lands on the target, what is the probability it will land on the shadedarea?

Answer 1

To find the probability, we will need to first find the area of the whole circle and the area of the shaded part.

Area of the Big Circle

Given that the radius, R, is 20cm, the area is

`\begin{gathered} A=\pi R^2 \\ =\pi*20^2 \\ =400\pi \end{gathered}`

Area of the Shaded Part

We can find the area of the shaded part by calculating the area of the small circle (r = 10cm) and subtract it from the big circle.

Hence

`\begin{gathered} a=\pi r^2 \\ a=\pi*10^2 \\ a=100\pi \end{gathered}`

The area of the shaded portion is

`\begin{gathered} A_s=A-a \\ A_s=400\pi-100\pi \\ A_s=300\pi \end{gathered}`

Probability of landing on the shaded portion:

The probability is calculated by

`\begin{gathered} P(A_s)=(A_s)/(A) \\ =(300\pi)/(400\pi) \\ P(A_s)=(3)/(4) \end{gathered}`

Therefore, the probability that the ball will land on the shaded area is 3/4.

The FOURTH OPTION is correct.