Question

A circle is inscribed inside a square. if a point inside the square is selected at random, what is the probability that the point will also be inside the circle?

Answer 1

$Let's\ find\ the\ areas\ of\ the\ square\ and\ the\ circle.\ The\ ratio\ of \\ the\ area\ of\ the\ circle\ to\ that\ of\ the\ square\ is\ the\ probability. \\ \\ Let\ each\ side\ of\ the\ square\ be\ 1\ unit. \\ \\ \therefore\ Area\ would\ be\ 1\ unit^2. \\ \\ Diameter\ of\ the\ circle\ would\ be\ the\ side\ of\ the\ square. \\ \\ Diameter = 1\ unit \\ \\ Radius = \frac{1}{2} unit \\ \\ Area = \pi r^2 \\ \\ = (\frac{1}{2})^2\pi = \frac{1}{4}\pi\ unit^2 = \frac{\pi}{4}\ unit^2$

$\\ \\ \\ Probability = \frac{Area\ of\ circle}{Area\ of\ square} \\ \\ = \frac{\frac{\pi}{4}}{1} = \frac{\pi}{4} \\ \\ \\ \therefore\ \frac{\pi}{4}\ is\ the\ answer.$

$\\ \\ \\ Thank\ you. \\ \\ \\ \#adithyasajeevan$