Question

H. W
1.
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 Im?​

Answer 1

$\frac {\pi}{24}$ is the Probability

Step-by-step explanation:

°Refer Figure attached, as the question is incomplete without figure.

Let us use the area to find the probability.

Now, Diameter of Circle = 1 m  

The radius of Circle = $\frac {Diameter}{2}$

= $\frac {1}{2}$ m

Now,

• Area of Rectangle =  Length $\times$ Breadth

= $3 \times 2$

= 6 $m^2$

And Now,

• Area of Circle = $\pi r^2$

= $\pi \times (\frac {1}{2})^2$

= $\pi \times \frac {1}{4}$

Now, The Die will be landed in the circle

= $\frac {Area\ of\ Circle}{Total\ Area}$

= $\frac {\pi \times \frac {1}{4}}{6}$

= $\frac {\pi}{6 \times 4}$

= $\frac {\pi}{24}$

Hence, The Required Probability is $\frac {\pi}{24}$

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer = π/24

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

➝ Probability that it will land inside the circle

$\rule{110}1$

$\huge\sf\purple{Steps}$

$\underline{\bullet\sf\orange{\:Area \: of \: rectangle:}}$

$\normalsize\dashrightarrow\sf\ Area \: of \: rectangle = length \times\ breadth \\\\ \normalsize\dashrightarrow\sf\ Area = 3 \times\ 2\\\\ \normalsize\dashrightarrow\sf\ Area = 6 \\\\ \normalsize\dashrightarrow\sf\ Area = \bf\ 6m^2\\\\\\\underline{\bigstar\:\textsf{\gray{Area \: of \: circle:}}} \\\\\normalsize\dashrightarrow\sf\ Area \: of \: circle = \pi r^2 \\\\ \normalsize\dashrightarrow\sf\ Area = \pi \times\ r \times\ r \\\\ \normalsize\dashrightarrow\sf\ Area = \pi \times\ \frac{1}{2} \times\ \frac{1}{2} \\\\ \normalsize\dashrightarrow\sf\ Area = \frac{\pi}{4}\\\\ \normalsize\dashrightarrow\sf\ Area = \bf\frac{\pi}{4} m^2$

❍ $\underline{\sf{\red{Probability \ of \ Event :}}}$

$\bullet$ Event : Chances of die will land under circle.

$\normalsize\ \dashrightarrow\sf\ P(E) = \frac{No. \: of \: possible \: outcomes}{No. \: of \: total \: outcomes}\\\\\\\normalsize\ \dashrightarrow\sf\ P(die) = \frac{Area \: of \: circle}{Area \: of \: rectangle}\\\\\\\normalsize\ \dashrightarrow\sf\ P(die) = \frac{\frac{\pi}{4}}{6}\\\\\\\normalsize\ \dashrightarrow\sf\ P(die) = \frac{\pi}{24}\\\\\\\normalsize\ \dashrightarrow{\underline{\boxed{\sf \green{ P(die) = \frac{\pi}{24} }}}}$

$\rule{170}3$