Lets assume first of all that this is a square bcuz the circle inscribed touches every side.
Let side be 4
Area of bigger square = 4*4 = 12
Area of bigger circle = 22/7*2*2 = 88/7
Radius is half of the side of sq
Area of the red portion = (12-88/7)/4 = 24/28
Side of inner sq = 4/√2
Area of inner sq = 8
Area of inner circle = 22/7*2/√2*2/√2 = 44/7
Area of yellow region = 8-44/7 = 12/7
Probability = favourable outcome / all outcomes
= Area of red region / area of all colored region
=
...
Let side be 4
Area of bigger square = 4*4 = 12
Area of bigger circle = 22/7*2*2 = 88/7
Radius is half of the side of sq
Area of the red portion = (12-88/7)/4 = 24/28
Side of inner sq = 4/√2
Area of inner sq = 8
Area of inner circle = 22/7*2/√2*2/√2 = 44/7
Area of yellow region = 8-44/7 = 12/7
Probability = favourable outcome / all outcomes
= Area of red region / area of all colored region
=
...
