Calculating Probability for Four Randomly Thrown Points
The area of the circle is given by A = πr^2. To find the area of one of the segments, we need to find the area of the sector formed by connecting two consecutive points with a line and the arc of the circle between them. This sector has an angle of θ = 90°, since the points form a square, and a radius of r. Using the sector area formula, we get:
A_sector = (θ/360°)πr^2 = (90°/360°)πr^2 = (π/4)r^2
Now, we need to find the area of the square formed by the four points. Since the length of each side is equal to the radius of the circle, the area is given by A_square = r^2. Thus, the probability of all points landing inside one of the smaller segments is:
P = A_square / A = r^2 / ((π/4)r^2) = π/4 = 0.25
So, the probability of all four points landing inside one of the smaller segments is 0.25, or 25%. Good luck and have fun tossing those points randomly!
