Suppose you drop a tie at random on the rectangular region shown
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 $\frac{\pi}{6}=\frac{\pi}{24}$.

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