Hello i need finding the probability

Each petal of the region is the intersection of two circles, both of diameter 10. Each petal in turn is twice the area of a circular segment bounded by a chord of length , which implies the segment is subtended by an angle of . This means the area of the segment is




This means the area of one petal is , and the area of is four times this, or .

Meanwhile, the area of is simply the area of the square minus the area of , or .

So



(provided these regions are indeed disjoint; it's hard to tell from the picture)