QUESTION

CSAT

Hard

Maths

Prelims 2016

A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.2 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability that the arrows fall in the red region of the archery target?

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Explanation

Given: Diameter of the target = $1$ m, so the radius of the target = $1/2 = 0.5$ m. The radius of the red band = $0.2$ m. The width of the remaining bands is equal.

Step-by-Step Calculation: Area of the whole target: Area = $\pi \cdot (\text{radius})^2 = \pi \cdot (0.5)^2 = 0.25\pi$ m². Area of the red band: The red band is a circle with radius $0.2$ m. Area of red band = $\pi \cdot (0.2)^2 = 0.04\pi$ m².

Probability that an arrow falls in the red region: Probability = $\frac{\text{Area of red region}}{\text{Area of the whole target}}$ Probability = $\frac{0.04\pi}{0.25\pi} = \frac{0.04}{0.25} = 0.16$ .