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 1m?
✓
Answer
Area of circle with radius 0.5m
A circle $=(0.5)^2=0.25\pi\text{m}^2$
Area of rectangle $=3\times2=6\text{m}^2$
Probability (geometric) $=\frac{\text{measured of specified region part}}{\text{measure of whole region}}$
Probability that tie will land inside the circle with diameter 1m
$=\frac{\text{area of circle}}{\text{area of reatangle}}$
$=\frac{0.25\pi\text{m}^2}{6\text{m}^2}$
$=\frac{1}{4}\times\frac{\pi}{6}$
$=\frac{\pi}{24}$
A circle $=(0.5)^2=0.25\pi\text{m}^2$
Area of rectangle $=3\times2=6\text{m}^2$
Probability (geometric) $=\frac{\text{measured of specified region part}}{\text{measure of whole region}}$
Probability that tie will land inside the circle with diameter 1m
$=\frac{\text{area of circle}}{\text{area of reatangle}}$
$=\frac{0.25\pi\text{m}^2}{6\text{m}^2}$
$=\frac{1}{4}\times\frac{\pi}{6}$
$=\frac{\pi}{24}$
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