Question

Given above is a figure of a dartboard, where the length and the breadth of the rectangle are respectively 7 feet and 6 feet, and the radius of the circle is 2 feet. The probability that a point chosen from the given figure lies inside the circle is:

• A. $\frac{\pi }{42}$
• B. $\frac{4\pi }{21}$
• C. $\frac{2\pi }{21}$
• D. $\frac{\pi }{21}$

Answer 1

The correct option is C

$\frac{2\pi }{21}$

Applying geometric approach to probability,
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
$=\pi \times 2^2=4\pi {ft}^2$
Area of the rectangle
$=7\times 6=42{ft}^2$

Thus, the probability that the chosen point is within the circle = $\frac{4\pi }{42}$ = $\frac{2\pi }{21}$
Or, the correct option is C.