Suppose you drop a dye at random on the rectangular region shown in the figure. Class 9

Suppose you drop a dye at random on the rectangular region shown in the figure. Class 9

Question 1.

Suppose you drop a dye at random on the rectangular region shown in the figure. What is the probability that it will land inside the circle with a diameter of 1 m? Class 9

Solution:

Area of rectangle = l × b = 3 × 2 = 6 m²

Diameter of circle = 1 m

∴ Radius of circle r = $\frac{1}{2}$m = 0.5m

Area of circle = πr² = 3.14 (0.5)²

= 0.25 × 3.14 = 0.785 m²

Probability (dye lands inside circle)

$\begin{aligned} & =\frac{\text { Area of circle }}{\text { Area of rectangle }} \\ & =\frac{0.785}{6} \approx \mathrm{P} \approx 0.131 \text { or about } 13.1 \%\end{aligned}$

∴ The probability that the dye lands inside the circle is 0.131.