Area of region 1/Total area = probability of a dart landing in region 1.

Because probability = desired outcome/all possible outcomes.

Area of region 1= ¹r²=¹r²=¹r²units².

Total area = area of the square=2r*2r=4r² units². (Each side of the square is 2r)

Area of region 1/Total area =¹r²units²/4r² units²=¹/4.

So the probability of a dart landing in region 1 is ¹/4.

The probability of a dart landing in region 2=area of region 2/Total area=

4r² units²-¹r²units²/4r² units²=r²(4-¹)/4r²=(4-¹)/4.

Verification: Probability of landing in region 1 + Probability of landing in region 2 must =1. So does ¹/4+(4-¹)/4=1? Yes, (¹+4-¹)/4=1.