Question

t hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartbozn, and the radius of the shaded region Is 2 in.the value 3.14 for T. Round your answer to the nearest hundredth.

Answer 1

Given:

Required:

To find the probability that the dart land will be in the shaded region.

Step-by-step explanation:

Area of the circle is given by the formula:

`A=\pi r^2`

Where r = radius

Thus the area of the circular region

`\begin{gathered} =(3.14)*(2)^2 \\ =3.14*4 \\ =12.56\text{ square in.} \end{gathered}`

The area of the square is given by the formula:

`=(side)^2`

Thus the area of the given square

`\begin{gathered} =(6)^2 \\ =36\text{ square in.} \end{gathered}`

The probability of an event is given by the formula:

`P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}`

The probability that the dart land will be in the shaded region

`=\frac{Area\text{ of the shaded region}}{Area\text{ of the square}}`

Thus probability

`\begin{gathered} P=(12.56)/(36) \\ P=0.3488 \\ P=0.349 \end{gathered}`

Final answer:

Thus the probability that the dart land will be in the shaded region is 0.349.