An equilateral triangle is drawn with its vertices if we put a dot in it without looking into the picture, find the probability of the dot being outside the triangle?
If the radius of the circle is r, then the side of the triangle will be √3r
Area of the circle = πr2
Area of the equilateral triangle =√34×(√3r)2 = √34×3r2
The probability of the dot being inside the triangle = √34×3r2πr2 = √3×3r24πr2 = 3√34π
The probability of the dot being outside the triangle = 1−3√34π = 4π−3√34π