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?

\frac{2}{7}

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\frac{π}{6}

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\frac{π}{7}

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\frac{1}{6}

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Solution

The correct option is B $\frac{π}{6}$
Probability of an event, $P (E) = \frac{A r e a o f t h e f a v o u r a b l e f i g u r e}{A r e a o f t h e c o m p l e t e f i g u r e}$
In this case, $P (E) = \frac{A r e a o f t h e c i r c l e}{A r e a o f t h e r e c t a n g l e}$
Area of the circle
$= π \times 1^{2} = π {f t}^{2}$
Area of the rectangle
$= 3 \times 2 = 6 {f t}^{2}$

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

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