Question

A circular area is marked on a rectangular patch as a target for a certain game. A player is declared winner if a ball thrown lands in the circular area. Then what is the winning probability for a participant given that the dimensions of rectangle are 2 m and 3 m while the radius of circle is 0.5 m?

• A. \(\frac{11}{84}\)
• B. \(\frac{11}{42}\)
• C. \(\frac{11}{179}\)
• D. \(\frac{5}{8}\)

Answer 1

The Correct Option is A

The total area of the rectangle is given by: \[ \text{Area of rectangle} = \text{Length} \times \text{Width} = 2 \, \text{m} \times 3 \, \text{m} = 6 \, \text{m}^2 \] The area of the circular region is: \[ \text{Area of circle} = \pi r^2 = \pi \times (0.5)^2 = \frac{\pi}{4} \, \text{m}^2 \] Thus, the winning probability is the ratio of the area of the circle to the area of the rectangle: \[ \text{Winning probability} = \frac{\text{Area of circle}}{\text{Area of rectangle}} = \frac{\frac{\pi}{4}}{6} = \frac{\pi}{24} \] Approximating \( \pi \) as \( 3.14 \): \[ \text{Winning probability} = \frac{3.14}{24} \approx \frac{11}{84} \]

The correct answer is option (A): \(\frac{11}{84}\)