Question:
Suppose you drop a tie at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?
Solution:
Given: Suppose you drop a tie at random on the rectangular region shown in figure
To find: Probability that it will land in inside the circle of diameter 1m
Total area of circle with diameter 1 m
Area of circle with diameter $1 \mathrm{~m}=\pi\left(\frac{1}{2}\right)^{2}$
$=\frac{\pi}{4} \mathrm{~m}^{2}$
Area of rectangle $=3 \times 2$
$=6 \mathrm{~m}^{2}$
We know that PROBABILITY $=\frac{\text { Number of favour able event }}{\text { Total number of event }}$
Hence probability that the tie will land in the circle is $\frac{\pi}{6}=\frac{\pi}{24}$.