# Ex.15.1 Q20 Probability Solution - NCERT Maths Class 10

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## Question

Suppose you drop a die at random on the rectangular region shown in figure. What is the probability that it will land inside the circle with diameter $$1\rm{m}$$? ## Text Solution

What is known?

A die is dropped at random on the rectangular region as shown in figure.

Length of rectangular region $$=3\,\rm{m}$$

Breadth of rectangular region $$=2\,\rm{m}$$

Diameter of the circle $$=1 \,\rm{m}$$

∴ Radius of the circle $$=0.5\,\rm{m}$$

What is unknown?

The probability that the die dropped at random will land inside the circle with diameter $$1\,\rm{m}$$?

Steps:

Area of rectangular region

\begin{align}\text{}& =L\,\times B \\ {} & =3\,\times 2 \\{} & =6{{\text{m}}^{2}} \\\end{align}

Diameter of circular region $$=1 \rm{m}$$ 

Radius of circular region $$=\frac{1}{2}\text{m}$$

\begin{align}\text{Area of circular region}&= \pi r^{2} \\ & =\pi \,\times {{\left( \frac{1}{2} \right)}^{2}} \\ &=\frac{\pi }{4}\end{align}

Probability that it will land inside the circle

\begin{align} \text{Probability that it will land inside the circle} & =\frac{\text{ Number of possible outcomes }}{\text{ No of favourable outcomes }} \\ & =\quad \frac{\text{Area of circular region}}{\text{Area of rectangular region}} \\ & =\quad \frac{\frac{\pi }{4}}{6} \\ & =\frac{\pi }{24} \\ \end{align}

The probability that it will land inside the circle is \begin{align}\frac{\pi}{24}\end{align}

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