Question

Given above is a figure of a dartboard, where the length and the breadth of the rectangle are respectively 3 feet and 2 feet, and the radius of the circle is 1 foot. What is the probability that a point chosen from the given figure lies inside the circle?

• A. $\frac{2}{7}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{7}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B $\frac{\pi }{6}$

Probability of an event, $P\left(E\right)=\frac{Areaofthefavourablefigure}{Areaofthecompletefigure}$
In this case, $P\left(E\right)=\frac{Areaofthecircle}{Areaoftherectangle}$
Area of the circle
$=\pi \times 1^2=\pi {ft}^2$
Area of the rectangle
$=3\times 2=6{ft}^2$

Thus, the probability that the chosen point is within the circle = $\frac{\pi }{6}$.