Area of square denotes the total probability, i. e, 1.
Area of circle denotes P(X ^{2 }+ Y ^{2 }≤ 1)
Area of shaded region denotes the required probability, i.e, P(X ^{2}+ Y ^{2} >1)
Area of shaded region=Area of square -Area of Circle
= 4 - ⊼
= 4 ( 1 - ⊼/4)
If area of square corresponds to total probability, then
4 sq.unit=1
= 1 sq.unit=1/4
= 4(1-⊼/4) sq.unit=
=1- ⊼/4
which is the required probability.