Question

Find the probability that a coin tossed falls in each of the shaded region. (all measures in cm)

• A. 0.66
• B. 0.25
• C. 0.2

Answer 1

Geometric probability = $\frac{\text{Area of specified region}}{\text{Area of the entire region}}$


$1.\text{Area of outer rectangle}=l\times b$
$=10\times 6$
$=60c{m}^2$
$\text{Area of inner rectangle}=l\times b$
$=4\times 3$
$=12c{m}^2$
$\therefore \text{Probability}=\frac{12}{60}=\frac{1}{5}=0.2$


$\text{2. Area of outer circle}=\pi R^2$
$=\pi \times 4^2$
$\text{Area of inner circle}=\pi r^2$
$=\pi \times 2^2$
$\therefore \text{Probability}=\frac{4\times \pi }{16\times \pi }=0.25$


$\text{3. Area of triangle}=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 4\times 3$
$=6c{m}^2$
$\text{Area of square}=2^2=4c{m}^2$
$\therefore \text{Probability}=\frac{4}{6}=0.66$